The need comes first.
Moses is doing someone else's work, keeping his father-in-law's flock on the far side of the wilderness. A bush is burning and not burning up. He says he will turn aside and see why. The text says God called his name when the LORD saw him turn aside. That 'when' might mark nothing more than the order of events. Still, the first thing Moses does here is notice.
Then God gives his reason. He has seen his people's misery in Egypt, heard their cry against their taskmasters, and knows their sorrows. Only then does he say: come, I will send you. Nothing about Moses is given as the reason. Why this man, the chapter leaves unsaid. What it does make plain is that the reason given is the people's suffering. One way to put it: the call runs on their clock, not his.
'Who am I?' meets 'I will be with you.'
Moses asks who he is to go to Pharaoh. God does not tell him he is able, or worthy. He says, 'I will be with you,' and gives him a sign. When Moses says he is slow of speech, the reply has the same shape: who made the human mouth? I will be with yours and teach you what to say.
The common reading hears self-doubt in these questions. Read that way, Moses keeps asking 'Am I enough?' and God keeps answering a different question: 'Will I be alone?' You could call that a dodge. Moses keeps objecting, so it did not end the argument. But the answers never once turn to his qualities.
One request finally changes something.
Who am I? What is your name? What if they don't believe me? I am slow of speech. Four objections get four answers, with no word of displeasure. Then Moses asks God to send by the hand of whoever he will send, usually heard as 'send someone else.' Only now does the LORD's anger burn.
Yet the call stands. In the same breath God names Aaron, who speaks well and is already on his way to meet Moses. Aaron will be his mouth. Was that the plan all along, or a concession? Anger and help sit in the same verse.
After that, Moses is not shown carrying this alone. Jethro sends him off in peace. Aaron meets him at the mountain, speaks to the elders, and does the signs. The people believe, at least that day. Pharaoh's refusal, though, was foretold from the start.
