Almost invariably, the first verse I write is not the first verse of the song.
The words that come to me initially are usually a distillation of what the song is about. The thrust of the song.
I don't like to lay out all the cards in the first verse, so what I'll do is use those song-defining lyrics at a more strategic "climax" point (like third verse before the last chorus, or whatever. Depends on the structure of the song.) And for the first verse I'll write sort of a prologue. Something that leads to, but doesn't totally give up, what the song is about.
So, in my mind, the first verse of the song doesn't necessarily need to be as strong as what you got in that initial Moment of Inspiration. Knowaddamean?
This may not have anything to do with what you're talking about, but I'm drunk and I'm on a roll!
Sorry
Chepney