Date range matching in ES

I would like to create a small scheduling app.

Lets say we have Joe and he needs to teach online multiple people individually about .. gardening.

He cannot teach more than 1 person at a time.

He has a calendar of 'available' dates and his 'customers' also have their own calendars.

Now lets say we have many 'Joes' and many 'customers' all trying to schedule their meetings.

I imagine we will have for the 'teachers' multiple date-range type, where I am storing their
'available' time.

and also a multiple date-range type for customers storing their 'available' time.

How would I start matching the calendar of these, 2 groups of people?

I do not think it is a good idea to do a massive query containing the full-range of available date-ranges of a customer to all the teachers or vice versa.

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