Are they permitted in USA?
If you're genuinely interested and you are eligible ring them up and ask.
Banks in the US aren't obligated to only accept SSN/ITIN for opening a bank account, but it is at their sole their discretion.
Some branches will let you, some won't. If you don't have these IDs you'll most likely be required by the bank to show up in person with the original valid IDs such as passport, DL, tax ID, etc.
But again it is at their sole discretion and you'll still require whatever paperwork they ask depending on the jurisdiction.
So they will require a local address in the US and potentially additional documents like PAN.
If you search online it does vary a lot from case to case, and in general HSBC Premier is
NOT recommended over any alternatives.
You will need to be tax compliant in the US and also India.
So don't open a US bank account on a whim just because you think it's cool or somewhat useful.