I am really glad to hear that there's interest, and hopefully I will have a 3-part series to share on this some time soon! Similar to Andrew's project linked down below, this is a 'true' home-brew receiver. I didn't know anything about DSP, etc, when I started out, so I learned a lot about signal processing (and the incredible techniques that make GPS work), and really hope I'll be able to publish it all soon!
Not OP, but in the meantime this may help alleviate your thirst for "how could someone do GPS from scratch", especially the end parts about radio signals and encoding: https://ciechanow.ski/gps/