You can set a minimum delivery period in hours, which will be taken into consideration before showing the earliest available delivery date or time slot to your customers. This can be done under the "Minimum Delivery time (in hours)" field under the General Settings -> Date Settings tab in the Order Delivery Date on the admin side. Minutes will be accepted in the decimal format like for 30 Minutes you can use 0.50.
Minimum Delivery Time can be set as 24 * number of days which needs to be disabled + the remaining hours of the current day.
Example: I want that the first available delivery date should be upcoming Wednesday for a customer who tries to place the order on Monday before 6 PM.
So, in the above example, 24 hours * 2 days + ( 24 – 18 hours ) = 54 hours which will be the Minimum Delivery Time if you want to allow delivery on Wednesday until 6 pm for a customer who visits the website on Monday.
Similarly, for the customer who tries to place the order on Tuesday after 6 PM the first available delivery date will be Friday.