It's possible but you still need to know what all your assets are before hand so itch.io can serve them. Using the godot/javascript bridge you can use the browser fetch api to download more assets (like .pck files) as the game is running. It's a bit overkill though, 99% of gamejams in godot do not need this. Just try keeping your assets under 200mb and you'll be able to export to web easily.
Ours is 224mb and we have to split it up but it's not too bad