Unfortunately, with that style of bridge, it's gonna take some relatively serious modification to mount a tremolo.
If it had a stop tailpiece (instead of the through-body string routing), adding something like a Floyd Rose FRX, a Stetsbar trem, or even a Bigsby vibrato would be as simple unbolting the existing bridge (and tailpiece) and mounting those to the existing studs.
As it is, you could remove the existing bridge and stud inserts, route a hole in the guitar to accept the tremolo of your choice, install the posts in the correct location and rout the rear for the springs and claw. You'd probably want to refinish the guitar at that point; at a minimum you'd have to do extensive touch up to make it look good. But that's a LOT of work to put into a guitar. If you were to pay someone to do it, I'm not sure what the bill would be, but probably more than the guitar is worth and as much as you would spend on a different guitar that already has a tremolo.
The simpler option, I guess, would be to install stud inserts where the tailpiece would be and use one of the options I mentioned previously. Lastly you could probably bolt a Bigsby B5 or something similar to the top behind the bridge, although if there's any curve to the top in that location it could make that difficult.
TLDR: Not easily or (probably) inexpensively, but there are always ways.