Has the statue itself been dated? 12,000 yo is the estimated founding date of Göbekli Tepe not it's last use. Humans like to move things about go through many phases of inhabitation of a place.
How is dating as a science faring in the replication crisis? It seems fraught with incentives for those involved. Discover something 2000 years old and no-one cares but 12,000 years old and you've got a TV career and a book deal.