They stood on the shoulders of people like Marian Rejewski, Jerzy Rozycki and Henryk Zygalski and many others who cracked Enigma with Polish ingenuity. They were the ones who originally had the audacity to think that they could crack the world's most sophisticated cypher technology with the meagre resources the Polish cypher bureau had.
That's true in part, but, IIRC, the Polish break relied on the original insecure operating practice that the Germans soon removed. The operator had to choose a "random" 3 letter session key. Using the day's settings, they'd transmit that key twice in a row (presumably because they were worried that errors might creep in), before adjusting the machine rotors to the session key and encrypting the message. Transmitting the key twice was a major security flaw, which the Polish attack relied on.
IIRC, the German army soon realised their error, and stopped the repetition of the key. This made breaking enigma much harder, which is where Welch(?) and Turing come in.