It's a good idea to try and get anchor bolts into the floor joists. Those rarely end up in the right places to line up with anchor holes. Good anchor strength is a big part of good security. When a safe can be put on it's side or back, burglary attempts are far more successful. 3/4": plywood may sound strong, but not really. When you have a 5-6 foot tall safe, you have a lot of leverage to push/pull and tear out anchors. A long pry bar under the edge with a close fulcrum point will pull even 1/2" or 5/8" bolts right out of 3/4" plywood real easy.
There are several ways to make this all better.
1. Drill some holes thru the back or side and lag-bolt into the wall studs. You can do this without making a mess if you use a large fender washer of steel plate over the holes. You may need to provide some shim blocks under the bolt-points against the wall so the safe is level.
2. If you have access the dead-area between the floors, use big machine screws (1/2" - 3/4") and place a large flat plate with the nut/lockwasher underside so there is a large bearing area to resist bole pull thru.
3. Place a thick sub base, maybe 3/4" good quality marine plywood under the safe. Use large flat-head wood screws anywhere you can get into the floor joists. This provides a much stronger foundation to then lag-bolt your safe down.
4. Same as #3, only use a steel plate, lag bolt it into the joists, and use machine-bolts into threaded holes in the steel plate.