Things We Actually Did:
Mercury delay lines were tubes full of mercury we sent vibrations through. Those vibrations would reflect around and get detected and read out later. This wasn't, technically, random-access, but it was memory.
Williams-Kilburn tubes were CRTs with long-persistence phosphor, the exact opposite of what display CRTs used, and metal plates on the front to allow the contents of memory to be read out. You could have two identical CRTs, one with the plate to use as RAM and one built into the display panel so the operators could see the contents of RAM in real time.
Core memory was tiny little ceramic ferrite doughnuts woven into complicated metal grids which would change how they were magnetized in response to a sufficient current; their state could be read back out non-destructively, and core was, in fact, nonvolatile. The core modules were woven by hand by women working with microscopes and very steady hands.
Being able to make usable amounts of memory out of components we can just etch into silicon was an amazing advance. Nothing short of revolutionary, really; computers as we know them would be flatly impossible without cheap, plentiful RAM.