Remember that the first mirrors were made from metal and polished volcanic glass.

Which means mirrors or mirror substitutes were always available to us even before we made metal tools as long as we could source obsidian. Granted you’d have to actually live near an active volcano for the latter.

However you aren’t wrong! A cheap way to make “mirrors” in the old time is to just take a flat bowl with mud lining the bottom and have water on top. This was used when volcanic rock of polished stone/metal was not readily available!