Archaeologists and linguists generally agree that Greek-speakers were already present in the Aegean by the time the Hittite kingdom coalesced in the 17th century BCE, and the Hittites and (Mycenaean) Greeks were contemporaries. There was interaction and cultural exchange between Hittite Anatolia and Mycenaean Greece, but one cannot say that Hittite culture "created" Greek culture.

I've touched on this in a couple of past posts.

• What was the role of the Luwians in Aegean civilization, and what do we know about Hittite-Mycenaean relations?

• What cultural and religious similarities did the Hittites, Luwians, Lydians, Phrygians and Trojans (indo European speaking bronze age civilizations in Anatolia generally) share with the Mycenaeans and later archaic Greeks which trace back to a pre-indo European substrate?

Further reading

• From Hittite to Homer: The Anatolian Background of Ancient Greek Epic by Mary Bachvarova

• Hittite Texts and Greek Religion: Contact, Interaction, and Comparison by Ian Rutherford