Is there a way to August our monthly Budget dates? Like to sync w CC's billing date?

Alternative is to request to adjust your credit card billing cycle to the bank/issuer. So your payment due date is at the end of the month. Most are able to adjust to billing at the beginning or early of the month. Usual cycle is 22 days.

Do note that they will ask you to pay the existing outstanding amount and for the next cycle, it may have two months of expenses depending on when the new cycle kicks in. Watch for late charges too.