Yes. It doesn’t even require especially dubious interpretation, just no one deciding enough is enough and putting a stop to it. And the basic combo even fits in a “Core + 1 book” environment—this really doesn’t require a ton of dubious interactions between disparate parts.
The key is the manipulate form ability of sarrukhs from Serpent Kingdoms. Serpent Kingdoms is a Forgotten Realms book, and it only works on a “Scaled One” native to Toril, so those are “issues” here, but neither requirement is a significant hindrance here, speaking hypothetically: we can just assume we’re talking about an FR game—which means everyone is presumably native to Toril—, and plenty of PC-eligible races count as “Scaled Ones.”
Anyway, manipulate form allows a sarrukh to give any Scaled One any abilities they themselves have, and raise that creature’s stats up to any number less than or equal to their own value in that stat.
And we can get manipulate form from any convenient polymorph magic that allows you to use the form’s supernatural abilities—for a lot of reasons, the shapechange spell is most convenient for this, but there are other options if you wanted.
The thing that was supposed to prevent manipulate form from being abused was that sarrukhs couldn’t use it on themselves. That’s why any route to Pun-Pun requires at least two people—a familiar, which can be presumed absolutely loyal, and conveniently shares your shapechange spell, is probably most convenient.
So once you have the ability to access manipulate form and a partner who can do so as well, the idea is that you become a sarrukh and manipulate form on your partner. You then stop being a sarrukh, and your partner can become one and use manipulate form on you. Since shapechange allows you to switch forms at will for as long as it lasts, it is doubly convenient, since you can swap back and forth without having to constantly re-cast polymorph magic.
The other part of the trick is to use items or spells to give yourself a bonus to something: that allows you to use manipulate form to increase your partner’s stats up to your (bonus-improved) stats. The advantage is that, while those bonuses won’t stack with themselves, once you use manipulate form on the other, those are their actual stats, not from bonuses. Which means you can trade the items over to them, and now the bonuses increase the value higher than your previous one, so they can manipulate form on you to get yours higher again. Rinse and repeat to get your stats as high as you want.
And since manipulate form can give your partner any ability you yourself have, and you have power polymorph magic, you can take on various forms, grant the abilities you want to your partner (who now has them permanently), and then they can go ahead and give them to you (now permanently).
None of this is at all dubious from the perspective of the rules as written. All of it is completely straightforward applications of manipulate form. Serpent Kingdoms was a notoriously poorly-considered book; the sarrukh and its manipulate form are far from the only absurdities in it (though it is by-far the worst of them). Earlier I said that the main limitation on manipulate form was that the sarrukh could not use it on themselves, but that’s not really accurate. The apparent thing the authors expected to prevent this nonsense is the fact that the sarrukh is an unplayable monster. As they so often did, they neglected to consider the possibility of a player getting access to monster abilities, i.e. manipulate form.
Now, various approaches to Pun-Pun do involve more tricks to allow you to pull the combo at lower and lower levels, and to get more abilities that might otherwise be inaccessible (e.g. class features that no monster has), and so on. Some of those tricks are somewhat more dubious, RAW-wise, than the basic combo.
One of the most famous renditions of Pun-Pun (the first one to work at 1st level) involves Pun-Pun as a kobold paladin who gets a wish off the demon prince Pazuzu, because you see, the description of Pazuzu says that the first wish makes someone Chaotic, and the second wish makes them Evil. Because Pazuzu delights in pulling down paladins, he always endeavors to give paladins everything they want with the first wish, to make it all go perfectly well for them, to try to encourage that second wish. One wish is all that Pun-Pun needs to get the combo going, though, and so the advantage here is you get one absolutely-untwisted wish. But this relies on an NPC description being absolutely iron-clad, on Pazuzu actually being a thing in your setting, and also on a 1st-level paladin knowing about this. People have some quibbles with some or all of that. But other ways of accomplishing 1st-level Pun-Pun, no Pazuzu needed, have been found since then. Even if you disallow all of those, if nothing else, a 17th-level character can just cast shapechange themselves, no wish required.
(For my money, though, Pun-Pun will always be a 1st-level kobold ex-paladin.)
So yeah, one way or another, Pun-Pun is 100% RAW-legal. It’s a fun little testament to the absurdity of the game, an occasionally-useful trivial answer to optimization questions (to illustrate the need for boundaries and constraints on the question), and possibly a challenging problem to work, to optimize it more and get the combo faster or more safely.
Pun-Pun is not playable. No one involved in figuring the combo out has ever recommended playing. In fact, I strongly doubt anyone ever has; it’s just pointless. Once you have achieved Pun-Pun ascension, you can literally do anything you want, with guaranteed success, with absolutely no concern for rules like turns or actions or resources. So even if it does happen it’s kind of like “OK, that’s cute; we’re going to ignore that you did that, and keep playing our game now, because we really don’t appreciate you summarily ending it on us like that.”