OK, having just skimmed through the module (which, since it's only 12 pp, didn't take long) I spotted the following things that would make this module as-written impossible (or at least practically so) for 1st level characters:
1) the 4-armed gargoyle in area 8 -- this thing has way too many hp and does way too much damage for a 1st level party to have any chance against it in combat; there are a couple of ways to bypass this area (ending up in area 7 and taking the secret passage to area 13, or going through the archway to area 11), but I don't consider either of those alternatives particularly realistic, because they both involve messing around with the archway, and IME a party foolhardy enough to be doing that is also likely to be doing other risky/foolhardy things that will get them killed sooner or later. A party that manages to avoid this area has done so by being lucky rather than smart (IMO), and luck will only take you so far in this module. Through this room and area 9 (#2 below) is IMO by far the safest/"smartest" route through the dungeon.
2) the magic bolts in area 9 -- each round spent in this room a magic bolt unerring strikes a random character for 1-6 damage unless he saves vs. spells; this is only a minor annoyance to high level characters (so long as they don't dawdle here), but is likely fatal to 1st levels (even if they're able to solve each secret door in a single round (very unlikely) that's still 7 attacks). This area can (theoretically) be avoided in the same ways as #1 above.
3) the stone gate in area 15 -- requires a magic ring to open; 1st level characters aren't likely to have a magic ring (unless they retrived it from area 13 -- but doing so would mean they'd foolishly have exposed them to the dangers of that room, which would almost certainly have killed them) whereas high level characters probably have at least one such ring, even if they're smart enough to have avoided room 13
4) the magical secret door in area 17 -- requires a gem of seeing (which can be gotten from area 11) or similar magic to "pinpoint the magic aura" and then a dispel magic or remove curse spell (both of which are well beyond the capabilities of 1st level spell-casters, and aren't found on any scrolls within the dungeon) to actually open -- this is the one truly insurmountable obstacle, because while 1-3 above are possible (if unlikely) for a 1st level party to successfully avoid/pass, this isn't -- you either have to have a cleric or magic-user of high enough
level to cast 3rd level spells or go home.
5) Acererak himself in area 33 -- a 1st level party doesn't have access to any of the spells that affect the demilich, and while conceivably a paladin could use the +4 sword found within the tomb and a thief could sling gems, considering the skull's -6 AC it's extraordinarily unlikely they could kill it before it had killed the entire party; however, while a 1st level party can't "beat" Acererak in combat, they can easily avoid combat with him -- steal his treasure and leave; which, for a party of 1st level characters in a level 10-14 module is certainly "victory enough"!
I distinctly remember fudging #2 when I ran this module for 1st level characters back in the 80s (I made the damage 1 point per bolt instead of 1-6); I obviously must've fudged #4, and probably fudged #1 and 3 as well, but I don't remember doing so specifically. My decision to fudge #2 was based on the fact that I wanted the fate of these characters to rest on their own decisions rather than arbitrary dice rolls.
The key to these players' success was that they were very careful about searching for traps and secret doors (and did so in ways that didn't rely on random die-rolls to succeed), and very good about avoiding red herrings and taking unnecessary risks. As I said before, I was fully expecting the module to kill these characters off in nothing flat (I rather assumed they wouldn't even make it past the first corridor -- and might not even make it to the first corridor!), and was amazed at how well they did -- which I'm sure is why I decided to fudge area 17 and allow them to keep going even without the necessary spells, because by that point they'd so exceeded my expectations that I was excited and wanted to see how far they could go, and didn't want to antclimactically and arbitrarily halt their progress over something completely independent of their level of play.
So, to answer the original question: no a party of 1st level characters can't "win" this module as-written, absolutely because of #4 (and very likely because of #1-3 and 5), but those are the only reasons, and only one of them is truly absolute -- everything else in the module is fully within the capability of well-played 1st level characters. And, probably needless to say, I definitely count myself as one who considers this a sign of how good the module is, not how bad it is.
