Christians Claim that the God of the Jews/ Torah is the Same God of the New Testament
When missionaries debate us, they claim that the God of the Torah is the same God of the New Testament. Jews say that their God is very different from the Jewish concept of God, since Jews believe in monotheism and the Christians believe in the Trinity, how are we to respond to the Christians?
It should be noted that there are vast soteriological (salvation), and doctrinal (creedal, ‘aqeedah) differences and disagreements about God between the Jewish faith and the Christian faith. For an indepth discussion on the numerous differences, please see the following lecture by Rabbi Michael Skobac. This lecture will provide you with many examples from which you can illustrate and subsequently prove your argument:
Now that we have firmly established that Jews disagree with the statement that their concept of God is the same as that of the Christian concept, we can now take a historical examination of the early Christian church and its views on the very same topic. Marcion of Pontus was the founder of an early Christian movement, dated to be between the period of 140 CE and 160 CE. This movement, named after him, the “Marcionites” were said to have believed that the God of the Old Testament was a violent, hateful, vengeful and evil God, while the God of the New Testament was one of love, grace and mercy. Marcion therefore taught that the God of the Old Testament was not the same God of the New Testament, thereby concluding that the God of the Old Testament was a quasi-deity, known as a “demiurgus” to the Greeks. We read from the Panarion, an early Christian work which documented the beliefs of the various Jewish and Christian sects, it says of Marcion and Marcionites:
Marcionites. Marcion of Pontus was the son of a bishop, but he seduced a virgin and went into exile because he was excommunicated by his own father. (2) Arriving at Rome he asked for penance from the < elders > of the time. Since he could not get it he grew angry and taught doctrines contrary to the faith by introducing three ﬁrst principles, a good, a just and an evil, and saying that the New Testament is foreign to the Old, and to the One who spoke in it.
The Catholic Encyclopedia expands on this and states:
We must distinguish between the doctrine of Marcion himself and that of his followers. Marcion was no Gnostic dreamer. He wanted a Christianity untrammeled and undefiled by association with Judaism. Christianity was the New Covenant pure and simple. Abstract questions on the origin of evil or on the essence of the Godhead interested him little, but the Old Testament was a scandal to the faithful and a stumbling-block to the refined and intellectual gentiles by its crudity and cruelty, and the Old Testament had to be set aside. The two great obstacles in his way he removed by drastic measures. He had to account for the existence of the Old Testament and he accounted for it by postulating a secondary deity, a demiurgus, who was god, in a sense, but not the supreme God; he was just, rigidly just, he had his good qualities, but he was not the good god, who was Father of Our Lord Jesus Christ.
Even if we were to disregard these evidences, we can use a Christian teaching known as “Progressive Revelation“, to prove that the Jewish concept of God is distinct from that of the Christian God. We read two definitions of this doctrinal teaching:
The things that God revealed to humanity were not all given at once. His revelation was given in stages……Progressive revelation means that God did not unfold His entire plan to humanity in the Book of Genesis or, for that matter, in the entire Old Testament. The Old Testament revelation, though accurate, is incomplete. The fullness of certain teachings cannot be found in the Old Testament. – 
Progressive revelation is the teaching that God has revealed himself and his will through the Scriptures with an increasing clarity as more and more of the Scriptures were written. In other words, the later the writing the more information is given. Therefore, God reveals knowledge in a progressive and increasing manner throughout the Bible from the earliest time to later time. This makes perfect sense since we know that not everything God revealed to us was revealed right away. – 
Summarily, this doctrinal teaching is meant to convey the belief that with each new revelation, God reveals more of His nature to us. Therefore, the nature of the God of the Old Testament is different and distinct to that of the New Testament because the God of the New Testament has had more of His nature revealed to us. An easy example is the Jewish God known as Elohiym which is in a plural form but is used to refer to one God, not many. With the advent of the New Testament, God allegedly revealed that Elohiym was used because God consisted of three persons united in one. This would mean, that at the time of the revelation of the Old Testament, Jews would have believed that God was solely one, and at the time of the inspiration of the New Testament, Christians would have believed that God consisted of three persons united united in one. Therefore, if we compared the two natures of the Gods at the time of their revelation/ inspiration, the Christians would be forced to admit that they would seem like two different deities because the teaching of their respective natures are at odds with each other. The JewsForJudaism response to Christian arguments that Elohiym means three persons united in one deity, is presented as follows:
“In form the word is a Hebrew plural noun; but it connotes the plurality of excellence or intensity, rather than distinctively of number. It is expressive of supreme or absolute exaltation and power. Elohim, as understood and used in the restored Church or Jesus Christ, is the name-title of God the Eternal Father. . . .”. This understanding of the word is quite different from that of Smith’s who, in his ignorance of the Hebrew language, rendered ‘Elohim, in Genesis 1:1, as a plural. Scripture teaches us that ‘Elohim, which is the plural of majesty, is used not only in reference to God, but also for angels (divine beings) and human authorities of high stature in society. This can be clearly seen, for example, from the following usage. Manoach, the father of Samson (Judges 13:22), after seeing “an angel of the Lord,” said: “We shall surely die for we have seen ‘elohim.” Concerning human authority, we read in Exodus 22:8: “Both parties shall come before the ‘elohim [“judges”], and whom the ‘elohim [“judges”] shall condemn, he shall pay double to his neighbor.” It is, therefore, ludicrous to infer from ‘elohim, in the first verse of Genesis, the existence of a plurality of gods. Where is the plurality of persons when a single angel, referred to as ‘elohim, visited Manoach? How can the Mormon Church explain the words of the woman to Saul when, upon seeing Samuel, she explained: “I see ‘elohim coming out of the earth” (1 Samuel 28:13)? Although ‘elohim is followed by the verb in the plural, it refers to only a single individual as is clearly seen from verse 14: “And he said to her: ‘What is his appearance?’ And she said: ‘An old man is coming up; and he is wrapped in a robe.’” Thus, even with a plural verb this noun may still refer to a single individual.
If the truth of the doctrine of a plurality of gods depends in any measure on the plurality in form of the noun ‘Elohim, the use of ‘Eloha, the singular of the noun, within the same context, most decidedly disproves it. The underlying reason for the grammatically plural form ‘Elohim is to indicate the all-inclusiveness of God’s authority as possessing every conceivable attribute of power. – 
Trinitarian Christians maintain that Genesis 1:26 and Genesis 11:7 are prooftexts of an alleged tri-unity god, but this claim is erroneous. The inference that “Let us make man in our image” (Genesis 1:26) refers to the plurality of God is refuted by the subsequent verse, which relates the creation of man to a singular God, “And God created man in His image” (Genesis 1:27). In this verse the Hebrew verb “created” appears in the singular form. If “let us make man” indicates a numerical plurality, it would be followed in the NEXT verse by, “And they created man in their image.” Obviously, the plural form is used in the same way as in the divine appellation ‘Elohim, to indicate the all-inclusiveness of God’s attributes of authority and power, the plurality of majesty. It is customary for one in authority to speak of himself as if he were a plurality. Hence, Absalom said to Ahithophel, “Give your counsel what we shall do” (2 Samuel 16:20). The context shows that he was seeking advice for himself’ yet he refers to himself as “we” (see also Ezra 4:16-19).
A misconception similar to that concerning Genesis 1:27 is held by trinitarian Christians with reference to the verse, “Come, let us go down, and there confound their language” (Genesis 11:7). Here, too, the confounding of the language is related in verse 9 to God alone, “. . . because the Lord did there confound the language of all the earth.” In this verse the Hebrew verb “did” appears in the singular form. Also, the descent is credited in verse 5 to the Lord alone, “And the Lord came down to see the city and the tower.” In this verse the Hebrew verb “came down” appears in the singular form. If a doctrine of plurality of persons is to be based on the grammatical form of words, the frequent interchanging of the singular and the plural should vitiate such an attempt as being without foundation or merit. We may safely conclude that the Bible refutes most emphatically every opinion, which deviates from the concept of an indivisible unity of God. – 
In conclusion, there are two main evidences we may use to demonstrate that the God of the Old Testament is not the same as the God of the New Testament. Early Christians such as the Marcionites held such a belief, and the Christian doctrine of progressive revelation teaches that the nature of God was believed to be one way and then later on known to be different and distinct from that earlier nature. These conclusively prove, without a doubt, that the Christian concept of God’s nature is and continues to be open to development. The question which the Christian has to answer is, ‘Given the doctrine of Progressive Revelation, what if God later reveals He is Five Persons United in One, would that mean the Trinity is false or that the Jewish belief in one God was also false?’
 – “Marcion/ Marcionites“, the Panarion by Epiphanius of Salamis. Anacephalaeosis III, page 228. Bold emphasis is ours.
 – “Marcionites“, the Catholic Encyclopedia (New York: Robert Appleton Company. 1910). Bold emphasis is ours.
 – “What is Progressive Revelation“, by Don Stewart, BlueLetterBible.Org
 – “What is Progressive Revelation and is it Scriptural“, by Matt Slick, CARM.Org
 – “Joseph’s Smith Translation of Genesis 1:1“, by Gerald Segal, JewsForJudaism.Org
 – “What is the Meaning of God said: Let Us Make Man in Our Image….?“, by Gerald Segal, JewsForJudaism.Org
and Allaah knows best.