Does Astral Heron played on the battlefield as the first card already reduce the cost of the next card?

Yes. You play Astral Heron as your first card. Once it's finalized on the battlefield, its triggered ability checks — it sees you've played your first card and that Astral Heron is now at a battlefield, so the trigger fires and gives the discount. Your next card (the second card you play that turn) costs [2][A][A] less.

So you play one card (Astral Heron) to get the discount on the next one. It does not discount itself. (FAQ #11829, #11821)