The Sphinx is a thousand years older than the earliest origins of Greek culture. It was part of their general historic/mythologic history just as it is of ours.
Believe it or not, nobody truly knows who built the Sphinx or even how old it is. Some estimates put it at thousands of years older than the pyramids. There is still an ongoing debates among academics and the not-so-academics who are trying to establish just the basics.
To tell the truth, it’s not clear to me that the Greek and Egyptian sphinxes are closely related. They’re both creatures with lion bodies and human heads. I suspect the Egyptians didn’t call theirs “Sphinx”. The name “Sphinx} or }Phynx” means “Strangler” or “Asphyxiator” in Greek, which suggests that this is how it killed its victims (although you wouldn’t think that appropriate for a lion-bodied monster).