Job to customer to calendar

Hi, I'm after something a little different.
if possible I want to take customers details or possibly even click an existing customer, then select a job length 1 hour to 8 hours and then send that booking to the customer so they can select the time and date they choose. I then want this to go to google calendar and availability to be from google calendar

so im looking at using a booking site like calendly to take new customers and have their details saved then preferably have a search or drop down of customers i can just select then select job length. customer should only have a time and a date to choose.

is this possible ?