Two parties are arguing with each other, but combat has not started. Perhaps leaders on each side are trying to avoid combat, but having trouble controlling their troops. Perhaps they were interacting in a friendly manner, but someone insults someone else and an argument erupts that could lead to violence. Perhaps two sides are competing toward completing the same goal (so they are hostile) but don't want to spend resources in combat with each other. Or perhaps there's just a loose cannon on one or both sides.
Both sides are aware of the other, and both sides are aware that violence could erupt at any time. The first three steps in The Order of Combat are:
Determine surprise. The GM determines whether anyone involved in the combat encounter is surprised.
Establish positions. The GM decides where all the characters and monsters are located. Given the adventurers' marching order or their stated positions in the room or other location, the GM figures out where the adversaries are—how far away and in what direction.
Roll initiative. Everyone involved in the combat encounter rolls initiative, determining the order of combatants' turns.
As I understand the surprise rules (and please correct me if I am wrong), the combat would not begin with anyone surprised. IRL of course, the person who swings first has a slight edge, though they can be preempted by a particularly fast opponent. But my understanding of RAW is that whoever initiates combat, the initiative roll completely determines the order. Acting first in this context becomes little more than a twitch that confers no advantage.
Are there any existing rules (SRD/core, expansions, Unearthed Arcana) which can model getting the jump on a suspicious or hostile creature who is looking right at you?
As a follow-on, I would take suggestions for how to model this in a simple way that doesn't do great violence to the existing rules.