It is possible to limit one order per customer for one week with our Maximum Products per User for WooCommerce. To do so, please follow the general instruction below:
1. At first, assign all of your products to a particular tag,
2. Then please navigate to WooCommerce > Settings > Maximum Products per User > General and set Mode to Product orders. Then set the Date range to This week and Order statuses to appropriate statuses,
3. Next, navigate to Products > Tags > Your tag > Edit and set the Limit per user to 1.
Please give it a try. If you have any other questions, then please let us know.