The angel of the LORD appears to Jacob in a dream (Gen 31:11), calls to Abraham from heaven (22:11, 15), and appears directly to Hagar (16:7-11; though calling to her from heaven in 21:17).
Here he appears to Moses in a flaming bush (Exod 3:2), yet Moses apparently sees only the bush burning, not an angel, until God speaks to him from the bush (3:3-4).
This is not the last occasion on which the angel of the Lord will act. The angel of God acts to protect Israel, moving the cloud to obstruct the pursuing army, in 14:19. In some passages, the angel speaks as if God, as apparently here (3:2-4; cf. Gen 16:10; 21:17-18; 22:11-12, 15-17; 31:11-13; Judg 2:1), whether as God’s agent (cf. Gen 22:16?) or because God’s name was in him (Exod 23:20-21). Some who saw the Lord’s angel also feared that they had seen God (Judg 6:22; 13:21-22; cf. Gen 32:30).
In any case, there should not be too much surprise at this point that the one speaking to Moses is the God of his ancestors (Exod 3:6) whose stories occupy much of our current Book of Genesis. Yet Moses hides his face lest he gaze on the LORD (3:6); he knows that no one can see God’s face (besides references above, see Exod 33:20). Moses’s fear here is quite different from his eagerness to see God’s glory in Exod 33:18, a request that the Lord grants albeit without showing Moses his face (33:20, 23; despite the idiom in Exod 33:11; Deut 34:10).