Unless something changed since the Playtest, you can't die in the first round of combat. You can only drop to 0 hp. At which point, you get to make several Death Saves with a possibility of stabilizing before you die.
If 2 PCs drop in the surprise round, generally the Cleric will take his first action to heal one of them, at which point they spring back up.
If one of the PCs that drops IS the Cleric that is admittedly unfortunate, but the PCs should then attempt to retreat, with the fallen PCs in tow.
And if a DM pushes for a TPK in the first combat of a new campaign, the DM is not running the game properly.
You die at Negative HP value.
The first encounter has 4 goblins and a bugbear who puts out damage a few points below the ogre.
If they get surprise (due to bad rolls etc) and roll normally you're looking at at least one dead PC because the bugbear can reduce direct to dead all of the pre-gens with a lucky dice roll.
On a crit he kills everyone. even the fighter.
If you want the OSR feel that's fine but...
The Starter Set doesn't come with character creation rules.
The Starter Set doesn't talk about what to do if this happens in the DM advice
The Starter Set adventure also penalizes you in XP, treasure AND consequences if you negotiate with the monsters (they are guaranteed to betray you, even if you make the deal after murdering all the others) - Straight up Keep on the Shadowlands style. or whatever the craptastic 4E first adventure was.
Now combined with
..The Starter Set is intended for new players and DMs
..The Starter Set is intended to set the tone for the new edition
this combines to form something that's pretty toxic if you don't have the Basic PDF.
I mean...if they wanted you to crunch through PCs like candy they should have given the 5 pre-gens and a few dozen blank sheets and a note to not bother naming your PCs until you hit 3rd level.
It's a solid enough module but it is written assuming the DM has an idea of what they should be doing.
If you run it AAW/RAW then..yeah. Expect death. The Adventurer's League first post after the set came out was "How do I record a TPK"