The first thing that comes to mind is mold. Mold spores are everywhere, they're just looking for a nice (for them) home environment.
Since you have the fan switch on "ON", rather than "AUTO", that leaves out the fan motor itself as a possibility of smelling, as if the fan motor had a problem, you would smell it all the time, not only when the compressor kicks on.
So the smell appears to go with the compressor in operation. With the compressor running, the evaporator gets cold, and moisture condenses on it. And that moisture could be the problem.
Since it is a very new installation, and this is the first A/C season for it, I wonder if there is an installation problem with respect to condensate drainage. Like air handler unit is tilted such that the drain pan cannot empty completely, leaving some standing water in it all the time. Or a drain line/trap not positioned properly doing the same. Or a partially plugged condensate drain line, etc. etc.
Others may disagree, but I think that running A/C with fan set to "ON" increases average humidity in an air-conditioned space as opposed to "AUTO", in which the fan runs with the compressor operation. Having a hygrometer, I can see that in houses I have lived in. The design of some two-story houses, where the main living area has a two-story tall ceiling, and a second-story balcony etc. overlooks the big space downstairs, often need to run the fan on "ON" to get air mixing. As opposed to a two-story house that has just a stairway opening to second floor, which minimizes warm air rising to mess up the conditions for a second-story A/C unit. In that case, if the second-story unit has air returns in each upstairs room, that's the best.
One inspection option (the company that installed the unit should really do this) is removing whatever panel to access the evaporator coil, and doing a careful inspection with a light, looking for black mold. Also to look into the supply plenum to see if mold has adhered onto the sides/top/bottom of the supply plenum. The supply plenum is the box attached to the evaporator/air handler on its output side. The supply ducts connect to the supply plenum. It may/may not be possible to see into the plenum from the coil area. It may require detaching the supply plenum from the air handler, and moving one side or the other enough to see into the plenum.
A word on "plenum" naming... the Supply plenum is on the output of whatever heats or cools in a forced-air system. The "Return plenum" is on the inlet side of the unit, it collects air from various return air sources in the house and presents it to the fan (blower motor).
The mold can be killed by spraying a water-soluble cleaner made for that purpose onto the evaporator coils/pan/ whatever, letting it sit, then flushing away with water. But its not a cure-all. If the friendly-to-mold condition still exists, it will come back eventually. If your A/C season will wrap up shortly, it might not be till next A/C season that the mold convention grows enough members to let you know.