I hate to say it, but that is why you upload as soon as you have something working. Especially if you use Butler (itch's upload software), you only have to upload changes, so it makes sense to upload everything early on even if you might not use those assets because it is much easier to remove assets than to upload more. Plus, it at least gives you something to work with.
You'll notice if you look at my submission that I have three versions. Basically, Archive, Unstable, Stable. First one you push is the 'archive'. This is your "If all else fails, I have something" branch. Next, you push unstable. This is your "This is my latest progress" branch. This could be a nightly or hourly push (you could even have separate nightly/hourly branches). Finally, whenever you reach a point where your game is stable, you push the "Stable" branch. This is you intended showpiece. If your experimental branch ends up proving stable, you can always make that your showpiece after the files are locked, but otherwise your stable makes sure you have something working.
TLDR:
Have at least three branches that you upload as you work on your project.
Archive: This is your backup/last resort. This is your first working game or the pieces leading up to that if you don't finish on time. This ensures you have something to show if issues crop up. You can also make a second archive that is your last stable branch (so one 'stable' version before your current stable version).
Unstable: This is your incrementally updated version. This is may or may not work, but it shows your latest progress. Upload this every x hours or upload it before the date changes.
Stable: This is your latest good version that you know works properly. You can always replace this with the unstable version later if the unstable version proves to work fine, but otherwise, this is your entry.