GA pilot with a Flight Instructor reported an altitude deviation during approach to HAF resulting in a CFTT event.

Narrative

On an IFR flight plan into HAF using the RNAV (GPS) RWY 30. NORCAL ordered us to 'cross JUMDA at or above 4000; cleared for the RNAV (GPS) RWY 30 Half Moon Bay'. I crossed JUMDA at 4000 from the southeast and began descent to 3300 per the approach plate. Just as I set power for descent and was leaving 4000; CFII told me to take my foggles off as we were approaching the overcast layer (OVC started around 2000). I had not anticipated how fast we would get to 3300 and we busted the altitude by 500 ft below. Descending to 2800 around 3nm from the FAF (WOHLI); CFII immediately caught my mistake and verbalized to climb just as we got a low altitude alert on our Garmin 650. I immediately added full power to begin climb back to 3300 just as NORCAL queried us on our low altitude. CFII responded to NORCAL that we were climbing back to 3300. We remained in visual conditions during this ordeal. I reestablished the aircraft on the approach and the rest of the flight was uneventful. Landing was butter.Cause: Multiple variables were at play for this flight but I understand these are not excuses. I mainly fly 6 pack aircraft but I have been building time in this TAA for my commercial rating. I also have not conducted IFR operations/training in quite some time so I was rusty. I most definitely hyper fixated on setting power/airspeed and lining up for the final approach course as my scan was significantly different within this TAA equipped with a wannabe G1000. Furthermore; once I crossed JUMDA; I had become oversaturated with beginning my descent; setting power/airspeed; lining up with the final approach course; and taking my foggles off to prepare to enter the overcast layer.Solution: I will ensure to rent one of my flight school's chairs for more chair flights prior to future IFR flights to practice the approaches and really become one with the aircraft. But I am sincerely sorry and have internalized this mistake; truly. Never again shall I bust.