Using security provider without Password

Is there a way I can use the security provider and security login without the users password? Here’s the scenario…

I have a users email stored in a MySQL database and use Firebase Authentication to handle passwords and social logins. On my login page, I have set up an API action on the server actions to query the users email and post the password to firebase. If the password is correct, firebase sends back a response like this:

{
  "localId": "ZY1rJK0eYLg...",
  "email": "[user@example.com]",
  "displayName": "",
  "idToken": "[ID_TOKEN]",
  "registered": true,
  "refreshToken": "[REFRESH_TOKEN]",
  "expiresIn": "3600"
}

How can I use this response to set the security provider to say the user is logged in?