I am not sure how other teenagers made this awkward transition, but I did it by writing a tiny assembler in Basic. It was fairly easy because Basic had PEEK (get contents of address), POKE (set contents) and CALL (jump to address) that everyone was used to using to get anything useful done. I think I just got tired of hand assembling programs into POKE calls.
I remember getting a thin wire-bound book with a detailed disassembly (with comments!) of the ROMs and DOS as a birthday present. I think one of the thing that inspired programmers on the Apple ][ was the amazing system code that Woz had written. He set a very high bar for assembly language programmers. His code was economical, fast, smart, and tiny. He demonstrated how to squeeze the most out of limited resources.