I thought they captured an Enigma machine from a submarine and reverse engineered it.
Or was that just “movie history”?
Movie history...read The Code Book by Simon Singh - a great treatment of the history of cryptography that discusses the Enigma puzzle very well.
Even if you do get an Enigma you can't decipher any message. You need the right wheels with the right positions and settings, and the right ring and plugboard settings, for that message or it's still gibberish. These settings were distributed in codebooks, and getting a codebook would of course only get you the messages for the timeframe covered by the codebook.
Getting the German military Enigma from the Poles gave them a starting point for actually being able to break codes by exploiting weaknesses in the encryption. Turing's contribution wasn't just in the code breaking itself, but in designing computers that could break the codes. His machine with his algorithm could eliminate most of the trillion-trillion possible keys for a message very quickly.
Both the Nazis and the Soviets were notorious for their mistake of persecuting brilliant undesirables, and look where it got them. Luckily for us Britain didn't go after Turing until after the war.