That he is the father will the judge still do a paternity test?

If he is willing to sign an acknowledgement of paternity, they may waive the test.

They may, is someone else challenging this, if another man is claiming to be the father they may require a DNA test. Also if there is reason to doubt, the judge can order it.
But since he is the father, a DNA test would not change the result.

No one else is challenging it