Serious Bible-believing Christian theologians debate this question. It's not entirely clear-cut; most theologians that I've heard suggest that it was not Ramses II (sorry, Cecil B. DeMille).
There is a fascinating bit of hard history that supports the accuracy of Scripture. Remember that Joseph (Mr. Coat of Many Colors) and Jacob, et al, were welcomed into Egypt by the Pharoah. Near the beginning of Exodus, there's a remark something about 'other Pharoahs who knew not Joseph' enslaving the Hebrews. (I'm going from memory here, so excuse me if I'm off a bit on wording.) Egyptologists have found that there was indeed a take-over in Egypt, in which a 'tribe' of outsiders threw out the longstanding line of Pharoahs and usurped the throne, establishing a new line of Pharoahs. The timing of that takeover is almost a perfect fit for the period between Joseph and Moses. Thus, there were indeed 'new Pharoahs who knew not Joseph'.
Again my words may be off a bit about Exodus, going from memory .... check it out for yourself.
The Bible is in fact a remarkably tight book vs archeology.
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