In games on that kind of hardware (I programmed a shipping commercial Super NES game which will remain unnamed) we seeded the randomness by how many frames it took the user the press a button after boot. On the PS1 (which also lacked a clock), we used user input timings plus CD load timings, since no two mechanisms read at the same speed.

Like I said, that's why games of that era weren't very random (and thus are especially amenable to speedruns and TASes).