High Speed trains first class

There are many high speed trains in October, which train and day are you looking at specifically?
Random train I am looking at, Oct 16, 13:20 Milan to Rome, has only 1 seat taken in 3 cars.

Probably looking too early.

https://www.seat61.com/Europe-when-do-train-bookings-open.htm

Trenitalia opens the bookings of high speed trains 180 days in advance, today + 180 = November 22.
FGaines, maybe you are misunderstanding discounted tickets with seats? Otherwise, Did you try to change car?

Could it be that only 2 discounted first class tickets are still available for that particular train? It's unusual for first class base fare to sell out so early. Some trains have other classes of premium tickets, such as business class and executive class.

Just making mention that a lot of us don't book first-class tickets as 2nd-class carriages are perfectly comfortable. Sure, if you can land tickets with little price difference between 2nd class and 1st then go for it but comfort-wise, it's not a big enough difference to pay a lot more $$ for.

You also don't say WHICH cities/actual dates you're trying to buy tickets for. From where to where? And are you looking at Trenitalia or Italo trains?