All additional puzzles will be accessed from either the campaign or with codes. It is impossible to add more puzzles to the current puzzle select screen since they take a lot of resources to render.In the current version of the game, are the puzzles on the selection screen the models used for the playable puzzles or a simplified version for display purposes?
However since the campaign has now taken over as the primary way to casually play the game, I might redo the puzzle select screen in a future update. I could make it more compact and text focused so that every puzzle is listed. Codes would then only be used to unlock the puzzle for the first time instead of every time.
If you hadn't noticed, this is Forum 2.0