Couldn't you fill the via with solder with a soldering iron before you place the chip if you're doing a hobbyist 4-layer process? Or do you mean the kind of hobbyist 4-layer process where JLCPCB solders the parts on too?
Hmm, maybe you could. I haven't tried it. You'd need to make sure that both sides of the via are un-tented (no green solder mask) so that the solder would flow through. The via would need to end up flat so the solder ball on the part would stick. And you still might get solder bleeding through when you reflow.
For high-ball-count FPGAs, it sounds super tedious to prep. And obviously it's a no-go for machine assembly. But for smaller stuff it sounds feasible!
