I've read that there are certain areas that seem to be impassable early, only to become possible after returning much later. Do I just have to go back later, or is there always a way to complete each puzzle on the first visit?
Every puzzle can be completed as soon as you can enter it.
Of course, some puzzles require a particular item to be unlocked, but assuming you were diligently collecting Sigils, as Elohim told you to, you should always have enough of them to unlock the item before even entering a puzzle area that requires it. If you try to solve one such puzzle, the game will notify you about retrieving the item first, so you'll know not to attempt an impossible puzzle.
There is however a door in hub world A, sealed with wooden planks, which you'll need an axe in order to get through. The axe can be found in hub world C, near the end of the game. If you want to complete the game 100%, a little bit of backtracking is therefore necessary.
Everything else can be completed the moment you encounter it. Some puzzles just require thinking outside the box, especially the stars which might require...
combining assets from multiple puzzles within an area
There are 5 items that need to be unlocked using Tetromino pieces (aka Sigils) before you can use them to solve puzzles.
- Connector - Located in World A. Allows you to connect laser emitters to laser receivers.
- Hexahedron - Located in World A. It's a box. You stand on it.
- Fan - Located in World B. Used to blow things (including you) around.
- Recorder - Located in World C. Used to record yourself doing things. Once you begin playback, you can interact with what the other you is doing.
- The Platform - Located in World C. Used while recording for the real you to place items (or themselves) on top of.
There is a sign by every puzzle showing which items you need to complete it. Items you don't yet have should be marked with red Xs.
Now, as for the Tetrominoes:
- Green (easy) pieces open up puzzles hubs (specifically Worlds A, B, and C).
- Yellow (medium) pieces unlock items.
- Red (hard) pieces are used in The Tower.
- Grey (extra hard) pieces are... a secret.