How to run wire through steel garage floor system
The common way of doing this is to use conduit and surface mount all boxes. The conduit provides mechanical protection (especially important for a shop) and the nice thing about this it keeps everything accessible, in case you want to add lights or a power drop for a tool or something later.






Alternatively, you may also be able to use MC (armored cable) wiring, though with a quick search I can't find a specific NEC reference to this, so probably best to refer to your local inspector / authority having jurisdiction (AHJ) to check.