If you have electrical experience then the first level is simply wrong. Your instinct should be to parallel relays' outputs where possible (less delay, less relay wear, fewer glitches, more similar to TTL logic), but the software does not support this.

My advice is to treat it like a puzzle: "how do you implement NAND in relays _if_ you can not do any parallel connections". When formulated this way, it is pretty easy to solve.

(The relays disappear in level 2 and we switch to digital logic, so "cannot parallel outputs" limitation makes much more sense there. I am guessing they didn't want to make up a new mechanic just for a single level, but I wished they'd explain it better)