Can I use premium processing with an employer that isn’t subject to the cap?

If your employer isn’t subject to the cap, you can file the petition using premium service, and in that case, absent any additional RFE, you should receive a result within 15 days. Once approved within 15 days, expect about another week to receive the approval notice by mail, and you should budget at least 2 weeks to prepare the H-1B petition documents themselves — so realistically, the earliest you could complete your interview would be about 1–2 months after you start preparing your documents.