What? You can use Cognito User Pools to sign-up and manage user accounts in-house. That's the core of any identity solution. You can hook up Google, Facebook, etc. as identity providers if you want to give your users a third-party sign-in option.

Maybe I'm misunderstanding your use case, so correct me if I got something wrong.

Yes, but you can't use it to allow users of your app to sign into another app or service that you don't own, using yourself as the OAuth provider. No "Sign in with MyApp" on another service/app.