I don't think I'd be allowed to entrust users passwords to an external entity, despite the fact that they would probably do a much better job than I would at securing them. Also despite the fact that we trust every other external provider to store passwords...
I've been looking into keycloak.
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.
Firebase does provide unlimited password logins for free, which mitigated my personal concerns about Auth0. The advantages of a SaaS auth provider compared to a roll-your-own have been documented elsewhere, and I personally found them compelling.
What are the reasons you 'don't like' something like Auth0?