Ask the GM, the rules are not precise and exacting
There are no exacting dimensions on the biggest medium creature or the smallest small creature and whether the first could squeeze into a space the size of the latter. You’ll have to ask the GM. That said, there are rules:
If you are not using a grid
Then a creature can squeeze into a space that it otherwise could not fit into but that a creature one size smaller could fit into without squeezing:
(…) A creature can squeeze through a space that is large enough for a creature one size smaller than it. (…)
What this means in terms of exact dimensions is never stated and so is up to the GM.
If you are using a grid
We know a little more about creatures and size as the section on Creature Size states:
Each creature takes up a different amount of space. The Size Categories table shows how much space a creature of a particular size controls in combat. (…)
Of course, this isn’t their physical size, it’s what they control during combat. That said, there are clear definitions of this right afterwards.
A tiny creature controls a 2.5*2.5 space
A small or medium creature controls a 5*5 space
A large creature controls a 10*10 space
A huge creature controls a 15*15 space
A gargantuan creature controls at least a 20*20 space
This doesn’t tell us how much physical space creatures of a given size category take up, so any real limit on squeezing has to be made by the GM, but it is some sort of start.
Personally, I abstract squeezing away almost entirely
If my party consists of medium creatures, I am simply going to design a dungeon with sections that either do not require squeezing, do require squeezing, or cannot be traversed even while squeezing. If there are creatures of various sizes, I’ll just decide which paths each size of creature can fit into. The exact dimensions don’t matter there.
The place I do use slightly more exact dimensions is when I simply apply the rules on control by letting a small creature squeeze into a 2.5*2.5 space and a large creature squeeze into a 5*5 space (such as to avoid an area of effect). Using this, a medium creature is unique in that squeezing mid-combat does not make it now control less space.