When I first downloaded Godot, I didn't donate because I had no idea if I'd even use it for long. After a year or so of using it, I came across various reminders to donate, and eventually I did (if I'm completely honest, literally just now). But most people will never come across that prompt again and will forget any need to. Its the same case with Elementary, or any other distro I've tried out. Why pay if I dont know if I'll even use it?
That being said, I can't think of any better way of asking without being obtrusive to the user. I guess you could have some really pointless badge or something you unlock by donating which could help prompt users later down the line, but I cant imagine the FOSS community would be a big supporter of that.