If the attacker is hidden, he does have advantage on the initiative roll.
Plus, they will have advantage on their attack, and anyone who tries to attack them will have disadvantage:
(While you have the Invisible condition, you experience the following effects.
Surprise. If you're Invisible when you roll Initiative, you have Advantage on the roll. [...]
Attacks Affected. Attack rolls against you have Disadvantage, and your attack rolls have Advantage. If a creature can somehow see you, you don't gain this benefit against that creature.)
All in all, I'm quite happy with this rule, even for an ambush. Combining advantage for the ambushers with disadvantage for the ambushees, the majority of the ambushers will act before their preys, with advantage. The couple of defenders who will get to act first wil have disadvantage on their attacks and won't even know where/who to attack. Still quite deadly, but not "you lose two turns, bam you're dead" deadly.