I think that if he couldn't come up with an explanation that makes sense, it's just time to part ways.

Invading each others privacy isn't the answer, trust is extremely important to relationships. If the condom came from the guy that previously owned the couch it would be fairly obvious. covered in lint, semen dried, likely holes in it, etc.

Besides, any person that cheats is going to be paranoid. if you had time to come write a comment like this, he had time to clear his phone and install secretive apps, delete numbers, pictures, etc. It's not going to solve anything and just erodes trust in the relationship. If a person is being shady, it will make itself apparent in time. If you don't trust someone/cant, it's time to end it.