Is this late or early? It's a bit unclear to me.
Because this question body wasn't meeting good quality standards of this site, I had to write this additional sentence.
Not a moment too soon implies that something happened when it was almost too late; just in time
Help arrived - and not a moment too soon.
Another minute and he'd have drowned; she found him in the pool not a moment too soon.
With this idiom, the five words are usually kept together. One may say
She arrived not a moment too soon.
But not (if using the idiom as intended)
She did not arrive a moment too soon. (incorrect)
Picky, I know, but it's idiomatic usage.
It is an idiom, and it is not helpful to try to analyse its literal meaning. The literal meaning is a sort of litotes, where "not too soon" means "almost too late".