Sure a 1st level PC CAN survive a fireball IF the spell rolls average AND they make a save. The point is that damage scaling in 5E goes up abruptly at 5th.
In my own game, my PCs are now 5th, but they recently took a liking to a 1st level "henchmen" who they bring along everywhere-- like a lucky charm. He is knocked unconscious every single fight, and has only survived due to a few lucky die rolls. I'm not a killer DM by any means. I'm just putting the pcs in level appropriate fights.
It sounds like this works in a lot of campaigns. But I can't imagine how without fudging rolls and creating soft fights.
I do ES@1 with character trees, and I have had level ranges up to a 1st-through-7th-level spread, and I love throwing large groups of opponents at my PCs without balancing them first (usually works out to Deadly x2 or worse). I do telegraph those foes so the PCs can prepare themselves or work around them, but usually they just batter their way through--and it's actually fairly rare to get a low-level character knocked unconscious or killed.
Can I make a wild guess and predict that the first-level henchman is wading into lopsided melee with a low AC? The one death we've had in our 4-month-old campaign was from an NPC ally doing exactly that, trying to take on 3 skeletons while the barbarian PC took on 4 skeletons. Since these skeletons got +4 to damage from necromancy, and the NPC had an AC of only 12 and 30 HP, the NPC took two rounds to become flying chunks of shredded meat (i.e. failed 3 death saves due to crits in melee). The players were pretty shocked how easy he went down.
Lesson: you shouldn't try to take on 3 enemies at once unless you are actually tougher than 3 enemies at once. 1st level PCs take heed. When you say "I can't imagine how it works without fudging rolls an creating soft fights," that's how. I play the monsters realistically, which means they have no clear idea who is high-level and who is low-level, and for the most part monsters like Slaads and skeletons and allosaurs will just attack whoever is closest in their attempt to rip off some juicy meat. As long as the low-level guy doesn't get himself attacked by multiple allosaurs at once, and he wears decent armor, he's probably going to be fine. (This is even more true if he plays tactically smart and throws daggers instead of charging into melee, but it's not strictly necessary--I have one player who likes to do zany dangerous things with his low-level guys, and has gotten knocked unconscious at least three times, but hasn't died with any of them. You can be a stupid heroic paladin fighting an allosaur with a sword at first level, in a battle full of allosaurs, and probably not die.)
P.S. Increased survivability at low levels in 5E is a mechanical consequence of several design decisions: 1.) PCs get full HP at first level (i.e. essentially double what they got in AD&D; there are no first-level fighters with 1 HP any more, they always have at least 10); 2.) death saves are a
very forgiving mechanic, and the gap between "unconscious" and "dead" has never been wider; 3.) the XP table has been modified so that instead of having to defeat 334 orcs to reach 2nd level, you now only have to defeat 3 to advance. Spending less time at level 1 decreases your chances of dying at level 1.