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