Hi KyleWatson-9987,
Agree with Manu, you can enable Teams for Education for Google users without an Exchange mailbox.
About Google Calendar, you could connect your Google Calendar with Microsoft Teams with Automate.io. However, you can only send a message via Microsoft Teams when there is an event in Google Calendar. For more information, please refer to: https://automate.io/integration/google-calendar/microsoft-teams.