Hello,
I am an Amazon AWS Connect expert with more than hundreds of successful Connect instance configuration and integration projects. Solutions which I delivered ranges from simple connect instance for small business to enterprise levels where we I had to design and implement integrations with Google services, Salesforce and custom CRM system.
With custom developed Lambda I can integrating your Connect instance with Google Calendar and I also can help you to have more effective solution and configuration in place by utilizing the Connect on the best possible way.