Given that to complete the signup the end-user gives you the newly select plain text password then your system could attempt a login with that password immediately after the signup. However, there’s some considerations around this as although signups can be done in a relatively straightforward way from your own system, the recommended approach for login would be to use universal login flow.
However, the above means that the end-user would be redirected and as such they would have to input the password again. If your system is making use of cross-origin authentication (which is not recommended) then technically this would be feasible as after the signup you would just call login with the password provided at signup.