Switch role on submit button

The exact solution depends on how you create a team. You will have to hook into that action. Supposing that creating a team is done by creating a post of the custom type “team” you would hook into save_post_team, leading to something like this:

add_action ('save_post_team', 'wpse314398_change_team_captain_role', 10, 3);
function wpse314398_change_team_captain_role ($post_id, $post, $update) {
  $current_user = wp_get_current_user();
  $current_user->remove_role ('Member');
  $current_user->add_role ('TeamAdmin');
  }

You can also keep the Member role, because users may have multiple roles in WordPress. You may also want to have a reverse function if you allow users to delete their team.