Actually, if you've watched TNG's early seasons, you've already heard this unused theme, in bits and pieces.
The very first piece of music heard in TNG ever (that isn't the intro itself) is a slower, less energetic (more introspective I guess?) version of that unused theme.
The main leitmotif itself appears all over early TNG.
I figure that, when Maccarthy was writing the early filler music, he assumed that his theme would become the main theme, and so heavily leaned into it when writing the filler music. Obviously, the main theme was tossed - but not his other music.

Hilariously it kind of makes me think of like The Orville - you know all those "Star Trek" themes without copyright issues.

Speaking of unused music, the final TMP/TNG theme itself was almost different:
https://www.youtube.com/watch?v=BbdhC-OXXa0

There's an interview where they tell stories, and apparently after they made this early version of the music, Robert Wise listened to it and gave the best three word critique ever - "There's no theme!"
Goldsmith basically went "...oh.", then went back and reworked what he had already into the 2nd version, and there you go that's the final theme.

Yea've I heard that before ... I didn't listen all the way through though ... yuck!!