The third law of entropy states that "the entropy of a perfect crystal at absolute zero is 0." However, the rationale for this requires some explanation. All equations governing macroscopic entropy treat entropy as a difference, never as a distinct value. This is very similar to how voltage is always handled as a difference. We assign an arbitrary voltage, ground, to be 0V.
With entropy, there is a more meaningful reference to be made. On the microscopic level, entropy is measured as the log of a ratio of "microstates." One counts the number of states the system can be in and still retain the "structure" being observed, divides it by the number of states the system can be in irregardless of structure, and you take the logarithm of that. By defining the entropy of an object with one possible microstate as having an entropy value of 0, we can connect the two systems in a meaningful manner. It just so happens to be that a perfect crystal at absolute zero has exactly 1 valid microstates with that structure, thus an entropy of 0.
Now, for the meat of the answer
You cannot consider a "squeezing" argument before the big bang, because there is no information about that time. There may have been no squeeze at all, it may have simply come into existence.
There is some bounding to be had. We know by the second law of thermodynamics that entropy always increases with time. Reversing this, this lets us know the big bang had to have less entropy than the universe has today, but this still doesn't tell us what we want to know.
To talk about entropy of the big bang, we need to use the other definition of entropy: we have to use microstates. Let's skip forward 10^-32 seconds; science isn't really comfortable modeling time before that. At that time, one can calculate the number of microstates available to that baby universe.
However, we have a problem.
We now have to determine how many microstates had the "structure" we need to claim it was a "big bang after the inflationary period." To answer this, we need to answer a very difficult question: how many possible configurations of the universe yield us to observe it? Without that number, we cannot actually calculate entropy.
Its a good thing you posted this on the Philosophy stack exchange. That question is one of the daunting questions of philosophy to this day!