You can't get a Cyprus bank account that fast, what you can is to receive the allocated account number and transfer money to that account but it is not accessible in any way before the account is approved by the bank and operative!!
So actually we don't advise to pay any money into a "only allocated" account number because it will make nothing than troubles if the account for one or another reason shouldn't be approved!
There are plenty of banks available in Cyprus i.e. Bank of Cyprus, Piraeus Bank, Hellenic Bank, FBME bank and so on.