If my opponent plays Challenge, can I play Punch first?

No, you cannot play Punch First in response to your opponent playing Challenge.

Reasoning

1. Timing: Both Challenge and Punch First have the [Action] keyword. According to Rule 334.1.a.1, cards cannot be played during a "Closed State" (when a Chain is active) unless they have the [Reaction] keyword.
2. Chain State: When your opponent plays Challenge, it is placed on the Chain, creating a Closed State. Because Punch First is an [Action], it can only be played when the Chain is empty (an "Open State").
3. Resolution: You must wait until the Chain is empty (after Challenge has resolved) before you can play an [Action] card like Punch First.

This interaction is consistent with RiftJudge FAQ #4454 and #6919, which clarify that [Action] speed cards cannot be played in response to other cards because they cannot be played while a chain exists.