Does Teemo Strategist trigger first before attacker can play an action card such as Punch First?

Yes, Teemo's defend trigger resolves first — the attacker cannot play Punch First before Teemo's ability goes off.

Here's the timing breakdown:

1. Teemo gains Defender designation → his "When I defend" trigger fires and goes on the chain.
2. The chain is now in a Closed State. During a Closed State, only Reaction cards can be played (Rule 338.1.a.1–2). Punch First is an Action card, not a Reaction, so it can't be played here.
3. Players get priority and may play Reactions (to buff Teemo, protect the attacker, etc.). If no one adds anything, the trigger resolves — Teemo reveals 5 cards and deals damage to the chosen enemy unit.
4. After Teemo's ability fully resolves and the chain empties, the attacker gains Focus and can then play Punch First — but the damage from Teemo has already happened, so the attacking unit may already be dead.

In short: Teemo's trigger resolves before the attacker gets an opportunity to play an Action like Punch First. The only window to respond during the trigger is with Reaction cards, not Action cards.