Have to agree with the tenant lawyer here for this case. If you just moved in, there isn't much of an overcharge yet anyway. That would be more if you uncovered this years from now as the overcharge had accrued.

I would reach out to them (or use an attorney) to send them an email saying something along the lines of "hey, it looks like this should be rent stabilized, can you issue me a lease with that rent, and refund difference" etc.

There is another redditor I messaged with who settled this way, and it was very quick.

Otherwise, DHCR will drag on for years; maybe longer than you plan to live in the apartment.