refinance isn't so complicated, but at first it can be overwhelming for sure.
Refi in general doesn't have a time frame. That said, many loan products do require a seasoning period. This means the lender wants you to wait a certain amount of time before they will lend. Sometimes this is a bank requirement, sometimes this is the underwriter requirement.
For instance, fannie mae (the underwriter for most residential mortgages) says they want you to wait 6 months. That is not a rule but it is fairly standard, (though there are ways around it).
Assuming 6 months from the time of a cash purchase to refi is a safe assumption.
as for your 70k, aren't you considering doing a BRRRR? use it for that!
I too need some clarification on the last "R" of the process. Is the purpose of the refinance to re-evaluate the homes appraised value and leverage against it for another flip the a HELOC OR home equity loan?