How can I ensure that the judges see thru my ex and see he is only trying to get out of child support

Child has resided with mother since birth. Parents were never married n split shortly after baby was born, father left was sporadically in childs life for months at a time, esp when child support was brought upon him. Father wants physical custody but the child has always resided with mother. Mother has no history of crime or drug abuse. False allegation filed by father from CPS case is unfounded. Mother has child majority of time. Father is a cop n mother is nursing student.

Father hasn't seen or interacted with the child in over 2 months. But yet he filed a petition for full custody after child support was in order a few months back. Will the judge see through this?