New tech makes this easy. Install Arc Fault breakers.
There are circuit breakers specifically designed to detect the conditions you are talking about. They contain a small digital signal processor that listens for the telltale sound of arcing. I talk like it's a sound, it really is - if you've ever had a loose connection on a speaker or headphone, you've heard it.
They are called AFCI breakers.
I imagine in a new build, your panel isn't CH, QO, or an obsolete panel like Pushmatic... so the AFCI breakers shouldn't be too expensive, probably in the $30 range.
If the house is super new, there's a good chance some of your breakers are already AFCI.
This won't hunt down the fault, but it will prevent it from burning your house down. when you get a trip, then you take apart each (now dead) outlet and look for trouble. There's no realistic way to find them in advance as they can develop over time.
If the breaker slot is already occupied by a GFCI breaker, you can either use a combo AFCI/GFCI breaker, or relocate the GFCI function downline to the first receptacle. Unfortunately AFCI receptacles are not common.
All my panels are the kinds where GFCI breakers are prohibitively priced, so I am fond of sticking a junction box 6 inches away from the panel and sticking GFCI receptacles there, then feed the LOAD wires back into the service panel to serve the circuit I'm protecting.