This is a common occurrence for websites using WordPress, the Divi Builder and The Events Calendar Plugin by Modern Tribe. When creating an event, the Gutenberg editor displays by default not allowing for any event options including start and end dates.
For Divi websites, you must use the classic editor to create events.
How to Enable the WordPress Classic Editor For Events Only?
In order to use the editor for events, you’ll need to enable it under Events –> General. Check the box to deactivate the block editor for your events. Once this is completed, you will see the classic editor and all fields return under the Add New Events.