The Sorcerer is, RAW, dead.
It's OK for PCs to die. Rolling up a new character isn't that hard once one has done it a few times. (When this happens, for the rest of the session I often invite the player make the dice rolls for the monsters and keep track of their HP, so that they have something to do to stay engaged with the adventure).
You and your friends create epic stories filled with tension and memorable drama. You create silly in-jokes that make you laugh years later. The dice will be cruel to you, but you will soldier on. (PHB, p. 4) ~ Mike Mearles {Italics Mine}
While I agree with the other answers' points about a DM-option to use average damage, I'll not base this answer on it.
The core problem was (1) tactical amplified by (2) "cruel dice"
The party didn't use a tactic appropriate to the ooze; some of that can be attributed to how often many of us who have played CRPGs or video games just wade in to slaughter monsters as a default behavior. (Been there, done that ...) Those habits are hard to break, in terms of forming a tactical approach to an encounter with unknown monsters.
Way back when dirt was new, and so was D&D, we didn't just wade into fights. We were tactically oriented on trying to set up a fight to our advantage; not doing so usually got a PC killed; using ranged attacks or long reach weapons, or obstacles and terrain, to keep some monsters at bay was something we strove to do. Teaching players to keep that kind of tactical thinking in their menu of options can take some coaching.
A related problem: the adventure was meant to challenge a party with the idea that the party would need to use their wits and good tactics to defeat a very hard monster (CR2 is a handful for a level 1 party), or to avoid it. Whether or not this is clear in the published adventure, or in guidance to DM's, is a matter of opinion. For new DM's, it is my opinion that both the Starter Set and this adventure could use more "How to DM and how to coach new players" guidance.
DM as coach
I have found over the years that part of being an effective DM is coaching new players. There are a lot of ways to do that. A few points to ponder as you present the party with more challenges in the coming sessions are where a little coaching is called for, and how to drop clues and hints about what is in front of them so that they have the information they need to (1) form tactical plans and (2) to "see" the situation more clearly.
There is a nice Q&A here about signalling danger.
Fighting an Ooze usually involves kiting.
What is kiting? Using your advantage of faster movement to attack and then move away from the ooze {or any monster}, usually using a ranged attack or a ranged spell attack. Some players need to be taught this.
While your new player won't necessarily know that, your more experienced players might have had some ideas about doing that from other games. (More on that in a moment).
Here are a few salient points about the Grey Ooze from the stat block.
Ochre Jelly
Speed: 10
Senses blindsight 60 ft. (blind beyond this radius)
passive Perception 8
When you combine the immunity to lightning and slashing damage, the tactical approach to defeating this monster is to used ranged attacks and to stay out of its reach at level 1. The party should "kite" it ... but how do they (the PCs) know that? They generally don't have stat block information in front of them.
The stat block information is meta-game information; as a DM, consider how to drop clues to the players that this thing is slow, and that the Barbarian's axe was not hurting it. Your description of what is going on is a key to them picking up on what the game world, and the monsters, are doing.
Clues and Ability checks; anyone can try any check
PCs grow up in the game world. While they don't have access to the MM or the DMG, they all grew up and learned various lore, stories and legends of the world that they live in. What they know is incomplete; just as with education in our world. They are wandering out into the unknown, so the sense of danger of not 'knowing it all' is part of the fun of adventuring.
Let's look at your party and see some ways on how to drop hints and clues.
Druid, sorcerer, monk, barbarian - and a level 1 warlock whose player was absent. {My note: Too bad, EB could have made short work of this ooze, kiting from range}
As the encounter opens, if the PCs withdraw and the ooze pursues them, they may notice how slow it is going. (I'll share an experience with that at the end). But they only will "notice" if you describe that slowness to them. If they move away from it and it can't keep up with them, they can attack from range: cantrips, thrown spears or daggers, thrown javelins, arrows, etc.
If the barbarian hits it with the axe and he notices "I don't think I am hurting this thing!!" that realization may need to be emphasized by the DM
You notice that you don't seem to be hurting it!
That means a change of tactics is called for. Or, you may want to have him roll for a Perception or other check to grasp/see that "I can't hurt this thing with my axe!"
Likewise, consider an ability check for the druid or the monk, or even the sorcerer: a History or Nature (Intelligence) check may, if passed, permit one of them to recall a factoid about the creatures known as oozes in this game world. I'd pick a DC between 15-20, depending on how much "common knowledge" of "conventional wisdom" or "Lore" is floating about your game world on stories of monsters: the true, the partially true, and the false.
Typical Difficulty Classes (Basic Rules/PHB; CH 7)
Task Difficulty______DC
Medium__________15
Hard____________20
They may, nor they may not, pass that check. If they do, you can offer some clues on the nature of this horror! Example: "You recall from your mentor," you tell the druid, "that gray oozes are immune to electricity!"
Enough on that: the "charge in and kill it" habit is a fine way for level 1 PCs to earn a PC death or a TPK. Coaching players on how to use terrain, and to think tactically, is sometimes necessary.
Even experienced gamers can screw up the tactics
Experienced gamers like me. I've been playing D&D since 1975, with a few breaks, and I made the same kind of tactical mistake that the sorcerer player made recently.
A bit over a year ago, my level 1 Ranger in the jungles of Chult, with a cleric, a barbarian, and a paladin in the party ran across some evil vines that, had either of them hit me, would have done enough poison damage to kill my character outright. I was engaging with sword and shield because one of them had grabbed/engaged our paladin. The two vines had slowly crept up on our encampment and then struck. (They passed their Stealth check, eh?) The CR of these vines was 3; a deadly + encounter for a level 1 party. As the battle commenced, I did not pick up on the DM's description about how the second vine was moving so slowly toward where we were fighting the first vine. I was in a position to get PWNED except that the cleric's player (@Shalvenay) called out "They are moving slowly! Get away from them, we need to kite these things!" He was thinking tactically.
I got myself out of melee range (Disengage). We eventually defeated the vines by moving and shooting: kiting them. It took a few rounds.