If you are serious about buying then find an agent whos the process.
I would be glad to help you
If the home is on the market and the offer is in cash, it can close as soon as you lift the inspection contingency. Cash transactions are typically very fast. If the inspection goes through and their are no repairs, I would say as soon as possible. Some banks need time to sign and review the contract so that could delay it a bit but their is no financing to worry about.
If there is a home you are interested in ask your agent to look into that. If the listing agent has done business with that bank or the addendums are online they may be able to answer your question for that specific property.