I would still purport (as others already have said, it's nothing new, or something I got out of the blue):
1. Playing technique, fingers. Leaning in... or not. Along the string. The sweet spot, after the bridge.
2. Pole pieces of a single coil passive pickup aligned under strings perfectly*. That narrow aperture plays huge role. As well as how strong, weak the pickup is. Inductance, resistance and so on. I would even go as far to choose Alnico over Ceramic but that's a tad hairsplitting and AR.
3. EQ, as people have said before. Where in the mids it occurs. Low mids, high mids...whatever. Just sweep for the sweet spot.
4. Compressor maybe, but it would be cheating, and a sort of ... trying to get something that is easily done in the first place, anyway, if everything else is right.
If you have a (type EMG, Bart) active pickup that is double coil and rails plus ceramic (i e humbuckers) and still get better punch, please let me know. I would be interested. You may get it, but I think it's way harder to achieve. You have to walk that extra mile, or light year. I think in the numbering list I wrote above, that point 1 and 2 are even, they go at a split first place, it's a tie.
Amp/cab would come at the very last spot on my list. Period. Not even on there, perhaps. I think those SD Quarterpounders, and G&L pickups with pole pieces and "hot" designs sounds like they have some kind of compression built in, so you don't have to use outboard compression to get that punch. I've also found out that the point 1 above with playing technique, to get that punch, is a slight trade off, and compromising dynamics, and accents of the notes. If you want to have punch at all times, you have to play and finger (pluck or pick) in a certain way that can get the dynamics and accents in any groove sort of compromised. But it's so with any compressor kicked in anyway.
* both along the string, sweet spot after bridge, and the width of the string.