You don't want the contract generated today. Always generate a contract early in a month to maximize the contract duration (you get the rest of Feb for free).

The process does take time. Once you sign the contract, expect a day or two delay before you can fund the UATP account. And another few days to get your "Welcome Letter" with your Tour Code and UATP card number. If everything works well, you should be able to book around Feb 7 or 8. No way to rush it, other than to make sure you get the contract on Feb 1.

(My answer is for Individual Flex members. Not familiar with the processing time for other types of contracts)