anyhow you can get a 12V PSU that does whatever amps (12? 15?) in a pretty small formfactor, and the "additional" stuff the motherboard needs is, as shown above, insignificant. The PSU can be pretty dirty, as in in the US do literal 10:1 winding to get 12V out (i know it'd be slightly different winding amount to account for losses in rectification and lines and whatnot but 10:1 looks nice to the math) and rectify it straight into one of those nanoPSUs. believe me i've seen me do it.
also don't ask to see my laptop DC-DC supply for running straight off a solar panel... it's larger than most NUCs, too. oh wait, you still need a laptop brick, plus the DC-DC. So you gotta DC-DC -> DC-DC -> laptop which -> DC-DC and probably DC-DC again (1.2v/3v3 rail probably clocked off 5v rail, that's what i'd do naively)
those "dashes" in "DC-DC" are doing a lot of heavy lifting
Had to do a repaste to get proper cooling.