Batman: The Animated Series went on HBO Max on January 1, 2021.

Quick context

The show originally aired on Fox from September 5, 1992 to September 15, 1995, and later became available for streaming on HBO Max in the New Year rollout.

Why this matters

If you were asking about HBO instead of HBO Max, the key point is that the series is associated with HBO Max streaming, not a first-run HBO channel premiere.

Source note

A later listing still shows the series available with an HBO Max subscription.