What’s cool about puzzles is that every time you find the spot where a specific piece uniquely goes, it becomes ever so slightly easier to find the next piece. If we think about it mathematically, for example for a 500 piece puzzle, each time you find a piece, that removes one piece from the pool of possible pieces. So if you took one piece at the start of the puzzle and were to try each piece at random for a specific side on that original piece you would have a 1/499 chance of finding it. Once you do, the chances of finding the next piece for a specific space adjacent to those would be 1/498, and the progress should look something like this graph:
This doesn’t factor in edge and corner pieces or the fact that only certain pieces can go in certain spots based on their shape (for example a piece with protrusions on all 4 sides can’t possibly go next to another piece with 4 protrusions).
To me there’s some comfort in knowing that every time you find the piece of the puzzle it’s only going to get easier from there. And easier, and easier, and easier. Yea it’s gonna be slow going for most of it and along the way you may hit some road bumps or miss some super obvious pieces, or you may rule out the right piece early on because it didn’t look quite like what you were looking for, but each piece, each bit of information brings you closer to the finished product, and the only way forward is to to keep plugging away.