“This sounds like a former leased car where the renter NEVER changed the oil…I would take Joe’s advise and MOVE ON”
As the OP has found out the hard way, used cars tend to be a crap shoot, based on how they were maintained by the previous owner(s).
But, beyond the usual unknowns when buying a used car…buying one that did not come with full maintenance records, and with a copy of the mfr’s maintenance schedule, so that you can compare the two, is an almost sure formula for disaster. Since the OP tells us that, " it had about 60k miles but we didn’t know the timing belt had to be changed around that time", I am going to assume that the car came with neither maintenance records nor a copy of the mfr’s maintenance schedule, which should have been an immediate red flag.
Or, alternatively, the car did come with a copy of the mfr’s maintenance schedule, but the OP failed to ever open the booklet to see what needed to be done, and when it needed to be done. Hopefully, the OP will come away from this experience with knowledge about what to do and what not to do when buying a used car.
Anyway–as was said, it is time to cut your losses and move on. If as much maintenance was skipped as I suspect, this car is like a ticking time bomb waiting to explode again inside the OP’s wallet.