You can sync your Gmail account with Outlook for Mac 2016 but you first need to add the account to Outlook. See Add an email account to Outlook 2016 for Mac for instructions.
Outlook for Mac 2016 currently doesn't support synchronizing your Google calendars, notes, tasks, and contacts.
Give us feedback about your need for Google support
If you'd like to see support for Google calendars, notes, tasks, and contacts in future versions, please visit the Outlook Suggestion Box to leave your feedback. We may not be able to respond to you personally, but we do review every comment.