Mobile SSO when you don’t know the Identity Provider

I have a mobile app that I'm going to allow users to SSO into. However, due to the nature of the business, the identity providers they'd use won't be common ones like GitHub, Google, or Facebook. It could be a bank, for example.

I'm struggling with the UX for this situation since I'm not sure how best to allow the user to select their identity provider. I can't provide a list of our identity providers and ask them to select theirs; management killed that idea.

How can I do this in a way that's user-friendly?

I was thinking of asking them for their email address, then using that to figure out which identity provider to use, but then they have to enter it again when they log in on the identity provider's site. Or, maybe asking them to use a token of some sort to identify their identity provider, and then setting the app to use that provider from now on. Is this a user experience pattern that's been done well before?