Here are some things to check if you were able to successfully (1) connect your calendars (see here for Google and here for Microsoft), and (2) create a sync connection but it appears that nothing is happening.
1. Make sure you are looking at future events.
CalendarBridge does not sync events that were in the past at the time of sync creation (except for recurring events that also extend into the future)
2. Check that you picked the correct source and destination calendars.
Each of your accounts likely has more than one calendar so double check you selected the correct ones. The calendars will be listed as “<calendar name> <account name>.” For example, “Holidays user@outlook.com,” is the calendar named “Holidays” on the account user@outlook.com.
For Microsoft accounts, the primary calendar for the account is always named “Calendar,” secondary calendars can be whatever the user named them.
For Google accounts, the default name of primary calendar is the account email address (i.e., it would appear in the dropdown as “user@gmail.com user@gmail.com”). Google allows users to rename their primary calendar, so the name of the primary calendar may be something other than the email address.
3. Make sure you have completed setup of a your Microsoft 365 mailbox. If your Microsoft 365 email address is brand new, you must login to it to complete setup of your calendar. A sign that setup has NOT been completed is that the account does not have “Birthdays” and “Holidays” calendars (which are created upon first login).
4. Confirm your Microsoft 365 plan includes Exchange Online (Microsoft 365 Personal and Family plans do not).
If you have connected one of those accounts to CalendarBridge you will see a calendar in the list of calendars — but that calendar cannot be synced to outlook on your desktop and that calendar cannot send or receive invites via your email address. (Yes, it’s very confusing and we are not sure why Microsoft does it this way)
5. Confirm you have connected the right Microsoft account.
Another confusing thing that Microsoft does is it allows you to have separate “personal” and “work or school” accounts under the same email address – And many people accidentally create a “personal” Microsoft account under their work email address without even realizing it.
If you are intending to add a Microsoft account setup by your work or school, make sure that you are selecting a “work or school” account during the login with Microsoft process. One way to tell is that, when entering your password, a login.live.com URL means you are logging into a personal account whereas a login.microsoftonline.com URL means you are logging into a work or school account.

Microsoft work or school account login

Microsoft personal account login
If none of these seem to be the reason your sync is not working, please submit a support request.