That's simultaneously true, and misleading to the point of being wrong. The earliest parts of the layers date that far back, yes. The features of Gobekli Tepe that people who aren't archaeologists actually care about like the obelisks date much later around the second phase of the neolithic (PPNB).

Also note that Gobekli Tepe is neither the oldest site we know of nor unique in having monumental architecture. Even within the Tepler culture, Karahan Tepe dates earlier and I'm sure you heard of the older site of Jericho.

From your link: "Radiocarbon dating shows that the earliest exposed structures at Göbekli Tepe were built between 9500 and 9000 BCE"

~9500 BCE + 2024 - 1 = ~11,523 years ago.

So yea not quite 12,000 years ago.

Oops, thank you - I can't read apparently!