May depend upon the age of the house.
Modern house ought to carry such loads.
call the safe 30x30, that's 900 square inches, or 6.25sf, 600#/6.5sf is only 92# per square foot, which is less than on "average" adult (yeah, you said 500, but I have experience with how full safes get).
As a practical matter, though, put a level on the safe and watch it for a few days, the floors may settle a bit.
If the upstairs closet floor is carpeted, note that there's (probably) a 1" wide tack strip on the floor at the wall--so don't push the safe up on top of it, or it will tilt--possibly more than a bit. (You may need to go source some wedges to level the safe in any event--a big box store, in the cabinetry area can help.)
Note, too, you probably have no more than 3/4" of subfloor to bit into to screw down the safe. Rather than fussing with lag bolts or the like (unless you hit a joist or truss) a toggle bolt may be your answer. YMMV