Yes, you can have FusionAuth simply federate identity and not hold anything permanent in its own datastore. SSO should work in that case.
Two options:
If your existing user store can speak SAML or OIDC, you should be able to use an identity provider
https://fusionauth.io/docs/v1/tech/identity-providers/ You would need to modify the theme and you'd probably want to use a hint.
If your existing user store can speak LDAP or a JSON API, you can use connectors without migrating (this is a feature for which you must buy at least a developer license, starting at 125/month, more here:
https://fusionauth.io/pricing/ ). Here's more on connectors:
https://fusionauth.io/docs/v1/tech/connectors/
In both these cases, FusionAuth communicates with your userstore through some kind of facade, not directly with the database. Such direct database access isn't supported.
I'm not sure how this will work for all aspects of FusionAuth (password expiration, passwordless, etc) but for the main login flows it should work great.