Firebase does allow you to integrate with other OAuth providers (e.g. Google/Facebook/Linkedin etc.), so you could perform some kind of validation on the google account, ensuring it comes from your company's mail domain? Just a thought.

Set up of these security schemes is not easy (took me a shamefully long time to get Firebase working with React-Admin and Hasura). I'd personally try and get a SaaS provider to work within your company's constraints before trying to roll your own.