H1B visa and expedited H1B processing

Hello !!
I want to apply for H1B visa and am in India right now. My USA employer (university) will apply to the immigration office for processing it. My question is, can they apply in USCIS Premium Processing category? I have never been to the states and don’t know much about visa rules. I know that one can go for this additional service during H1B visa extension process while being there but not sure in a fresh visa case.
My employer is ready for the additional costs but I am not sure if I am eligible to go for this premium processing category. Any suggestions/ comments are really appreciated.
Best, Manni

Yes, you should be eligible for PP.