I have a 2007 Malibu, it will only start on a jump start.

I bought the car second hand but I think it is the original battery. I had it to a garage and the say the battery is fine..

The mechanic is after going through all the wiring, they cannot find the problem.

I had a problem similar to this with my 06 Chevy malibu. I ended up having to change my starter. Before I went through a trial and changed my alternator and battery as well not knowing what I needed to do. But I’m order to test your alternator. While the car is running. Take your battery posts off of the batter. If the car remains to run your alternator is fine. Also you can get a screw driver and stick the to the pully part of the alternator. If it sucks in it like a magnet then it is fine. If that is okay then like I said. I would check your starter.