Can I kill an enemy with Archery with Haldir before the Archery effect occurs?

No

afaik you dont have an action window between the beginning of combat phase and having to deal the archery damage

The timing doesn't work, as Rajam says, there is no action window before the Archery damage. The same problem comes up with SneakAttack+Gandalf, there is no way to have him soak some of the Archery damage, and if want to use his direct damage effect to kill the archery source then you have to do it in an earlier phase, so he isn't still around for combat.

Thanks for the answers, friends!