This here is something that really really annoys me about how 5e does its surprise stuff: as far as I'm concerned if you're that surprised you shouldn't even GET initiative until the first attack has resolved.
Why must the attack be finalised before you get a chance to react?
5E is very clear that upon hostilities erupting there is a slight chance you might be able to do something (if youre quick enough, and have a relevant reaction to use) even if surprised by (say) an invisible dragon breathing fire.
The dragon breathes a masive line of flames, and you notice the blast coming your way. COmbat is triggered. You roll initiative. A dex (reflexes) test.
If the dragon wins, he goes first and youre toast. No reactions or actions possible (youre surprised). Then its your turn (you cant do anything, but can now take reactions). Then on turn 2 the dragon flies over and full attacks you (to which you might be able to cast shield or use the parry manouver). After that you can finally take actions.
If you win (roll higher on initaitive), you still cant take actions on your turn (you have to sit there like a drooling idiot while you get burnt to death) but might just be able to use a reaction to raise your shield in time (if youre a shield master fighter) or cast absorb elements (if youre a wizard) when the dragons firebreath is resolved on its turn.
If you're surprised by the whoosh of close-range arrows in the air you're not even going to get your shield up before they arrive, never mind do anything else of use.
Thats what the dex (initiative) check is for. Maybe you will, maybe you wont. If youre particualrly alert (the alert feat) are a high level barbarian (feral instinct) a champion (superior athlete) or have a really high dex, it all helps.
Also, turn it around: the party spend ages setting up an ambush - all goes well, they get the drop on the foes, all the stealth and perception checks come up aces for the party - and due to poor initiative rolls half the opponents get to react and-or attack before the party does. Ridiculous.
Dude, a surprised creature cant attack before the party. They miss thier first turn.
So your ambushing PC's trigger the ambush. The enemy are surpised. Initiative is rolled.
Assume the bad guys go first. They cant take any actions on turn 1 (aside from stand there like grinning idiots). The party attacks first.
If the bad guys rolled crap for initiative and the party win, they have to endure 2 x attacks from each PC (one on turn 1, then the monsters turn 1 theyre surprised and cant act, and then another round of attacks on turn 2).
If you housrule some extra attack to occur outside of the combat round sequence, that could mean up to three attacks against a surprised creature before it can react. In 5E, thats a death sentence.
Far better would be that the surpriser automatically acts before anything else happens, then rolls regular initiative with everyone else.
They aready do get an automatic action on turn 1. Surprised creatures cant act on turn 1. So it doesnt matter if they roll a billion on that dex check, theyre copping an arrow to the face first.
The Dex check (initiative0 is just to see if surprised creatures can possibly still take split second
reactions before getting an arrow to the heart, and to see if they have to endure 2 x full attacks before acting, or just the one.