To prevent past dates, try to gather the requested date before the form submission and use that selection to show or hide the form button — making it only visible if the selected date is on or after today. You’d bring the date value over to your form submission by adding a column value in the form screen.
You could also do this by using a pre-defined list of dates in your form, and filter the choice list to only include values on or after today. This may not be feasible though unless you’re only looking to allow certain dates to be booked.
See this post for more info: Super Simple Sign-up App with limited time slots