Does DayBack Sync to Google Calendar
Introduction: DayBack's Advantage
DayBack shows your Google Calendar items and your Salesforce, FileMaker, or Office.com items in the same view so that you have one place from which to make your scheduling decisions. You can create and edit both Google and Salesforce, FileMaker, etc. items from within DayBack, and you can do this with not only your Google calendars but any that have been shared with you.
So DayBack does not two-way-sync your other events to Google Calendar.
However, you can share your calendars and write actions that will push events from other calendars to Google, so these events block out your availability in Calendly.
Option 1: Sharing
If you need to publish and share events to users outside of your DayBack group--folks who don't have access to your Salesforce org, for example--you can use the sharing feature in DayBack to create URLs for any view in your calendar. This is great for sending customers their project timeline, or sharing schedules with employees or contractors. Details and a short movie of this in action are here: https://dayback.com/publish-share-schedule/
Option 2: Push Events to Google Calendar
Think of this as a one-way sync.
Using DayBack's custom event action, you can send select events from your other calendars to Google. Any changes made in Google aren't sent back, so this isn't syncing, but it's a great way to mirror some of your Salesforce or FileMaker events in Google. For example, you may send a subset of your events to a new Google Calendar to keep your Calendly availability up to date. Learn more here: Push Events to Google Calendar.
AppExchange apps that will sync to Google Calendar
There are a few Salesforce AppExchange apps that will do this alongside DayBack...
Appirio will sync events to Google on the hour, but they can not sync custom objects.
Cirrus Insight will also sync your event to Google and does support custom objects.