Reuse existing salesforce login

We have a reactjs web app where we configured new universal login and added support for email/password, google sso and salesforce sso logins.

This app is loaded as an iframe in salesforce. When a user wants to use our app in salesforce, here is the flow:

  1. Open salesforce and login.
  2. Open our app in a tab inside salesforce.
  3. Perform salesforce sso login again in our app.
  4. Use our app.

Instead of performing login twice, is it possible to reuse the login performed in salesforce directly?

Current code:

const App = () => {
  const {isLoading, isAuthenticated, loginWithRedirect} = useAuth0();

  useEffect(() => {
    if (!isLoading && !isAuthenticated) {
      // check if salesforce login has already happened
      // if so, skip loginWithRedirect and reuse existing login
  }, [isLoading, isAuthenticated])