Can I remortgage a property immediately after cash purchase?
With regard to how and when you can remortgage, the method of purchase is irrelevant; buying with cash doesn't make any difference to the property's mortgageability. What is relevant is the lender's attitude to remortgaging a property recently bought.
Almost every BTL lender has a six month ownership restriction, preventing you from applying for a remortgage before you've owned the property for that period.
Commercial and specialist lenders don’t operate that restriction, so will accept applications at any time.
If you want to remortgage, irrespective of whether you bought for cash or not, it is quite simple; you use a lender that allows you to.
Another level of complexity enters the equation if your intention is to remortgage at a higher value than the purchase price paid. To do this almost certainly will require you to have improved the condition of the property since purchase in ways that are obvious to the lenders surveyor. No improvements = no increase in value - and that usually means no mortgage, or at least not against a higher value than what you paid.