Similar to Calendly (https://calendly.com).
This is an API where you can create a public calendar and let others book meetings with you based on your availability.
There is optional Google Calendar integration available. To integrate Google Calendar, create a public google calendar which the API can access to create events for you.
Follow the steps at https://docs.simplecalendar.io/find-google-calendar-id/ to find your Calendar ID.
Pass this calendar ID while creating a new user using the API.