By default, the booking system allows bookings up to the Start Date & Time of the Event, to prevent bookings being made before that time, you will need to use Unpublish Date & Time function.
- Go to Settings > Events
- Find the events in question (by using the filters as required)
- Select the Events you want to modify
- Click on Actions and select " Update Event Details"
- Click "Update unpublish time of selected events"
- Use the options to set the Unpublish time as required.
- Click "Confirm"
More details:
- Publish and Unpublish Events