It's actually more nuanced but yes.

Check a map of Neanderthal migration and concentration. They returned to the Levant in mass numbers.

Sumerian tablets call them The Old Ones.

The Fertile Crescent was Celtic. Celts mixed baboon DNA into the Neanderthal in Dilmun to "unmake them".

You'd need to study Sumeria for years like I have to start seeing the bigger picture.