Hello Jan,
Thanks for reaching out to us!
I can think of 2 ways to get the events out from The Events Calendar.
You can do an iCal export. You can find the button on every calendar page that creates the ical feed for you.
Potentially this snippet would be useful for you, which will allow you to export the events for a custom date range:
https://gist.github.com/andrasguseo/b8e2739b11fdbd2d5ebacce23d862046
The other possibility would be using the REST API endpoint of The Events Calendar.
The endpoint URL looks like this: http://yourdomain.com/wp-json/tribe/events/v1/events
Here you can find an article that can help you get started with this:
https://theeventscalendar.com/knowledgebase/introduction-events-calendar-rest-api/
I hope this helps! Let me know if you have any further questions.
Cheers,
Andras