The DH does not appear in the official count until he bats, irrespective of “lineup” order.
Applied Ruling:
Mets start tomorrow’s game with Peralta at pitcher, Bichette at third, Robert in center, Benge in right, and Polanco at DH. Upon the first pitch of the game, all of those players except Polanco enter the count, ordered in their spot in the batting order: Bichette, Robert, Benge, Peralta.
In the bottom of the first, the Mets are retired in order and Polanco does not bat.
In the top of the second, Polanco falls into a hole while being chased by a wild boar and breaks an ankle. Vientos replaces him as DH in the bottom of the second.
Polanco returns 6 months later and next plays in September. He enters the record then, and not at all on March 26.