Question:

Muslims often claim that the New Testament was corrupted very early on, is there any proof of this?

Answer:

The Qur’an in Surah 2, Ayah 79 mentions that a people from among the People of the Book forged writings and claimed these writings to be from God:

So woe to those who write the “scripture” with their own hands, then say, “This is from Allah,” in order to exchange it for a small price. Woe to them for what their hands have written and woe to them for what they earn.

In this case, people were forging writings and claiming them to be scripture from God. As per the question being asked, we do have extremely early evidence from Paul (or someone writing in his name), claiming that letters and teachings bearing his name were being falsified by heretics during his lifetime. We read this in 2 Thessalonians 2:1-4:

Concerning the coming of our Lord Jesus Christ and our being gathered to him, we ask you, brothers and sisters, not to become easily unsettled or alarmed by the teaching allegedly from us—whether by a prophecy or by word of mouth or by letter—asserting that the day of the Lord has already come. Don’t let anyone deceive you in any way, for that day will not come until the rebellion occurs and the man of lawlessness is revealed, the man doomed to destruction.

Therefore, Muslims are not making this claim without evidence. This is a Biblically based belief, from one of Christianity’s earliest sources. I hope that this answers your question.

and Allah knows best.