I didn't test it but probably

  DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/1000/bus \
  DISPLAY=:1 \
  sudo -H -u normaluser \
    --preserve-env=DBUS_SESSION_BUS_ADDRESS,DISPLAY \
  firefox

I'd add -H to the options of sudo to make it set the home to normaluser's one.

I assumed that your DISPLAY is :1, which is what my Debian has set for me. That's another variable that you could read from the environment of Firefox.

You might have to pass/preserve other environment variables to make Firefox work.