Islam was founded over 700 years after the foundation of Christianity.
In fact Prophet Muhammad was directed to refer to the people of the book (Christians) if in doubt of the Quran’s revelation.
So, the finality of the book (the Bible) is confirmed by the Quran itself.
Quran 10:94
“So if you are in doubt, [O Muhammad], about that which We have revealed to you, then ask those who have been reading the Scripture before you. The truth has certainly come to you from your Lord, so never be among the doubters.”