Is it possible to have the AI spawn after the player spawns?

Yes

Could you tell me how?

There are a couple of ways to do it. Do you want the AI spawn to be delayed only for the first human spawn? If so, when your map starts to load, disable AI spawning: Only on the first human character spawn (many campaign maps do this, look at their scripts), reenable AI spawning: I should point out that a server running this map will be stuck on it until a human player joins the game.

Does this go in my lua, and if so, where?

This is probably over your head to be honest. You need to understand lua scripting to do what you're wanting to do. Again, this is going back to keeping it simple.