The main post has the technical details, commentary begins here.
The revised language leaves interpretation pretty open here, especially with respect to when the combat begins.
PHB24’s text mentions, then flinches, ambush tactics as an example. Ambushes are not really mentioned again, just a fleeting mention that seems to leave it up to a case-by-case ruling.
Any creature unaware of its foe at the start of combat has the Surprised condition, thereby rolling the Initiative ability check at Disadvantage.
There are a couple of questions needing answers: a) when exactly does the combat “start”? and b) is a party a single “foe”?
Let’s say a highway robber steps out from the shadows as a dozen arrows drawn by a dozen longbowers ignite, illuminating a ring of ambushers around your party. The robber steps forward, flourishing their rapier in a “hand over your jewels” way as flaming arrows are loosed. Your party can see all of the attackers, so no one in the party is Surprised and - probably - has already started planning for combat. Everybody rolls Initiative normally - but when do those loosed arrows start making contact? Remember, firing the arrows was the first overtly hostile act and Initiative wasn’t rolled until after they were mid-flight.
In this case, I think my ruling would be that the inbound arrows demonstrate an attack against the alert and aware party of heroic adventurers, so the combat begins the moment the arrows are loosed. A combat round is 6 seconds (won’t take that long for the arrows to travel) of simultaneous turns. The arrows will certainly arrive on their marks at the start of each character’s turn, so a Saving Throw is appropriate to avoid damage.
Next scenario is similar, but the robber steps out and no lights reveal hidden longbows. Arrows are launched from Invisible attackers at the backs of each individual party member, unaware of the incoming attacks. The party is aware of one hostile, but the combat is being initiated by undetected foes. Does the visibility of the distracting robber matter? What if they didn’t reveal theirself until after the arrows flew? When, exactly, does this combat begin?
Obviously this one is complicated, and I doubt there’s a satisfying (or even satisficing) way to codify this. To me, the robber’s visibility is a part of the ambush, drawing the party’s attention away from the arrows flying at its back. The party rolls Initiative at Disadvantage because the attacking foes are more unnoticed than seen. This combat is going to begin at the moment the party becomes aware of the attack: as the arrows either find or miss their respective marks, determined by a per-arrow ranged attack roll vs its target’s AC and resolved all together, before the first round of combat. Character feats that enable them to sense and respond to unperceived attacks should get resolved with the attacks.