This is the chapter in which Moses gets derailed by God from his shepherding of sheep to shepherd Israel, i.e., the one with the burning bush. The event itself is not necessarily Moses' conversion, but I think it draws a fitting picture of what is going on in it.
First, there is the burning bush, then Moses sees it. He is the only one around to see it, we are explicitly told that "the angel of the LORD appeared to him," (verse 2) i.e., Moses. So the bush is specifically for Moses to see and, it would seem, for him to be drawn toward, which he does. Who wouldn't? I suppose someone with a phobia of fire, or bushes, might not have, but that misses the point. Here is a strange appearance that would draw crowds in that day, not having advanced special effects and pyrotechnics, and it is in the middle of nowhere. Moses does not appear to have been seeking God, and the bush appears to be there whether Moses wanted to find God or not. So Moses comes out, sees this amazing thing, and did what anyone in his place would do "And Moses said, 'I will turn aside to see this great sight, why the bush is not burned.'" There may be a sense in which Moses could have not gone to see the burning bush, but if so, it is the same sense in which most people could not take a raise without any bad side effects (as having to move, etc., might be). In the same way, in salvation, the one who was lost--wandering the wilderness, not even, necessarily, wanting to see God--sees a great light, a strange glory, and, though it may feel like a choice, it is a choice with no question as to what they will choose.
Despite the unsurprising nature of Moses reaction to seeing the bush, the text says "When the LORD saw that he turned aside to see, God called to him out of the bush, 'Moses, Moses!' And he said 'Here I am.'" So there does seem to be some sense in which God responds to our actions. This does not seem to me to be a difficult thing to resolve, although it seems worth its own post. In short, God is beyond of time, as the transcendent God, but this does not mean that he is not also in time. There is a sense in which he is God with us, and in that way he acts as is right for him to act given what has happened up to a point in time.
God then introduces himself to Moses. Verses 5 affirms God's holiness and verse 6 reminds that he is the same God as has been working to bring this people into being. Verses 7-9, then, express God's compassion on his people. In verse 10 God calls Moses, telling him what he now wants him to do. Moses has already come to God, he does not need to do this thing. Except that God is able to be the power for Moses to do it, as is shown in the following verses. This is similar to a Christian being saved. We are told to do things, but our power to do those things is entirely God's power. Thus, the response to sin is to seek that God would use his power "for it is God who works in you, both to will and to work for his good pleasure." (Philippians 2:13)