A week ahead of check-in, since it takes longer than typical Prime deliveries.
For our last trip, we placed our order on 11/22, it arrived at our resort 11/27. We checked in 12/1, and the resort had our Prime Pantry box sitting on the table in our room when we got there. We ordered waters, cheezits, and toiletries.
We are checking in 5/22 for our next trip. I plan to place my Prime Pantry order on 5/15. This time we are mostly ordering beverages - waters and gatorade - because space in our car is limited and those items are the heaviest/bulkiest.