Is there any connection?

In the Babylonian creation myth Enuma Elish, Anshar (also spelled Anshur), which means “sky pivot” or “sky axle”, is a sky god. He is the husband of his sister Kishar. They might both represent heaven (an) and earth (ki). Both are the second generation of gods; their parents being the serpents Lahmu and Lahamu and grandparents Tiamat and Abzu. They, in turn, are the parents of Anu, another sky god. If this name /Anšar/ is derived from */Anśar/, then it may be related to the Egyptian hieroglyphic /NṬR/ (“god”), since hieroglyphic Egyptian /Ṭ/ may be etymological */Ś/.

The Sanskrit noun avatāra is derived from the verbal root tṝ “to cross over”, joined with the prefix ava “off, away, down”. The word does not occur in the Vedas, but is recorded in Pāṇini (3.3.120, 4th century BCE). Avatāra was initially used to describe different deities, then around the 6th century AD it began to be used primarily to describe the manifestations of Vishnu.[11] While earlier texts mention deities taking on different forms, the Bhagavad Gita (4.5-9) is the first text to discuss the doctrine associated with the term even though the word avatāra itself is not mentioned.