Yep, they should have trouble even getting to the safe in the first place, alarms. motion detectors, exterior lighting, cameras... Ethel Kravitz across the street...
If it where me....Coated long wood screws with fender washers into the floor and the wall...thieves give up pretty easy if it isnt a smash and grab job....and moving a safe down stairs is no easy job.
Ive seen concrete anchors pull out easier than regular ole drywall screws.
Assuming the floor is carpeted, you can pull the carpet back to look at the sub floor. The plywood/OSB joints should line up over the floor joists. Plus the screws/nails inside the perimeter of the sheet should tell you where those joists are. Mark the locations on your wall, put the carpet back (may need to be restretched -- would be the only down side) and then layout your holes, predrill, and lag down.