I am not aware of any sorting/demotion by release status. Oh, you can filter by it, but if you hit https://itch.io/games the games in that list are all games, from prototype to released and even cancelled games.
If you have a closed beta or something like that, you might want to have restricted access.
But as soon as you are ready to face the public opinion of whomever stumbles upon your page, or whoever visits because of your promotion, you can publish your project.
Can I make it public without publishing and showcase the progress?
I do not understand this sentence. It make no sense to me. Itch does not have publishing/release dates as Steam has them. You can't showcase a thing, that no one can see. And you can't have public feedback, if a thing is not public. If you wanna do a closed beta test, that is a different thing.
But sure, you can talk about some things in regular community threads, without publishing a thing. But the old devlogs are deprecated. The way to do this, is to publish a prototype and maybe create devlogs about that project. But all this ties in with what I wrote earlier: you need to have an audience to get feedback.
Maybe make a side project and join a game jam.