TJI is a manufactured wooden "I beam," It has solid wood top & bottom "flanges" with a dado to receive a glue-lam "web" between the flanges.
They are an efficient (and "green") method for framing houses. They span long distances economically.
Unlike traditional solid lumber joists, they do want some planning before just scabbing in additional framing.
Now, for OP, TJI are typically sized to fit the span, so, they often are over-built (without the size, the spacing, and the span, that's hard to know). So, a "mere" 800# safe might not be an issue. Spotting the safe near exterior walls will improve the support, too.
Now, where crawling under the house might be to advantage, would be to double-up the subfloor. Fitting some 3/4" plywood glued & screwed to the bottom of the existing floor would give more "meat" to allow bolting the safe down.
Using the garage does invite some questions about climate, as noted above. Dehumidifying rods do not much help above 70-80° especially at high humidity levels. Those rods (which are very much like aquarium heaters) are not going to help much below 40° either. Garage "slabs" will want careful examining, too. A test hole drilled near the proposed safe location to determine the actual thickness of the slab is something I always recommend (6" expansion bolt is going to be middling useless in 3.5" of concrete).