No.
The quantity of addresses is MUCH MUCH TOO BIG for humans to ever use them up. The probability of two humans ever having the same properly generated address in all of human history and future is effectively zero.
What about the bitcoin address collider experiment thing, where they have claimed to find up to 3 different addresses with funds on them? I remember reading about this, but I can't find more details. The website of this thing is:
https://lbc.cryptoguru.org/aboutThey seem to have passed the 1000 trillion mark.