New HVAC installed. Why does it blow fuses?

Since its a new unit, and you didnt have this problem before, I venture to say that the power wires feeding the unit voltage are somehow touching some metal conduit somewhere, like they were accidentally cut or a wire came loose inside somewhere in the conduit. But only touches it every so often.

The problem is obviously electrical. I would say that since it is a new install that the grounds aren't properly checked. I can guarantee that the next thing they say is that you've got a faulty circuit board from the manufacturer. If you can't have the original installers fix your problem under warranty, then the only thing you have to go off of is internet advice.... Have the grounds checked.

P.S.

A ground would only be a secondary symptom. Other wires being loose would cause the ground wire to blow a fuse so that someone isn't electricuted. That is what ground wires are for. Safetys.

The heating circiut is of course the problem. 80% of the time it is the fault of the contractor with the remaining 20% being a factory problem. 100% of the contactor saying it ain"t his fault!! I mention this so you are forewarned.

Now to the actual problem: the thermostat wiring and or the thermostat would be the likely culprit here. The next issue of the main tripping before the unit breaker did is another indicator of improper wiring

You might need an additional breaker added to your box.

Your main box is overloading. Did you buy any new appliances etc.etc.