Can I solder on my own RAM for 2014 Mac Mini?

I doubt you can since there are many connections like hundreds on each module and you risk overheating components on the board removing the old ones and risk damaging the new module when soldering the new ones in.

The circuit board is soldered by inserting the components and soldering all at the same time with a process like wave soldering

https://en.wikipedia.org/wiki/Wave_soldering

If you have special reflow soldering gear for ball grid arrays

and X-ray viewers to ensure proper soldering of the tiny BGAs

(since all connections are underneath the chips and between

the PCB and chip, therefore not visible to the eye), certainly you can.