Hey there @Michael16643 - thanks for your post!

There is no way to get the invitee booking confirmation, no, unless you yourself are also an invitee. 

Example: if this is a Group Event Type, you can set the invitee limit to one+ more than you’d like to see sign up, then take that extra slot yourself so that you receive the invitee booking notification (email confirmation). 

Otherwise, every time a booking is made in Calendly, the host receives an email confirmation as well. It looks a little different than the one the invitee receives, as it includes answers to any Invitee Questions On Your Booking Page etc., but this email can be forwarded as needed and comes from notifications@calendly.com.

At this time, however, there will not be any way to ensure you see each email confirmation that goes out to an invitee upon each booking made in your Calendly organization. I’m sorry! 

I hope this helps!