It’s often heard that different universes could have different physical properties than our own, but could our own universe have been wildly different as well? Scientists have discovered much about the conditions very soon after our Big Bang. Given what we know about the conditions in the earliest time after our own Big Bang, could those conditions have produced a universe with different physical properties? Certainly there’s many ways for all the matter to end up distributed differently, but what about things like physics, chemistry, and math? Was it inevitable that any universe produced by our Big Bang would have identical kinds of photons, quarks, electrons, protons, neutrons, atoms, etc., and that the atoms would always combine the same way, and math would always work the same way, forces work the same, and so on? Or were there different ways things could have progressed and the particles could have different masses, forces worked different ways, etc?
There are two things in your question.
The precise values of the physical constants may well be able to vary. But you get a chicken and egg problem in that our understanding of those first few moments is predicated on our understanding of our known physics. We don’t have a grand unified theory, so the precise nature of what might have been going on at energy levels where full unification was still present isn’t known. But what we do surmise and calculate is based upon the numbers we do have. We still have no idea about as disparate things as the scale problem, or the goldilocks nature of other physical constants. So of which affect such fundamental things as whether atoms can form at all. Maybe there is a range of values some constants might range across, and then you get to invoke the weak anthropic principle - basically if they did vary for what we have, we wouldn’t exist to see them. So we only exist to see those values that allow us to exist.
The other part is “and math would always work the same way”. I don’t think anyone has any idea what it could mean for math to work any other way than it does. You could posit a universe of a wildly different nature, different number of dimensions, more or less forces, but if you want to count things, you will end up with Integers. And the rules for numbers will be the same, and the rules for manipulating numbers, and the rules for manipulating the rules for manipulating numbers will also be the same. The alternative universe may not be usefully described at any scale by Euclidean geometry, but the abstract rules for Euclidean geometry would still exist and work exactly the same as they do here. You would not be able to find a universe where some numbers had more than one distinct set of prime factors, nor find one where Pi equalled 3. That would not be a different universe, but a different reality.
Nobody knows. We have no understanding of why the relevant physical quantities have the values they have in the first place. And without knowing what governs those values there’s no way to know how else they could have turned out.
There’s plenty of theoretical work in this area, and I believe there was a recent thread chewing on theories that revolve around quasi-random universes and the anthropic principle, but there are others. Many theories run into testability issues. It is also possible that our own universe doesn’t yet have the values it’s supposed to have. We could be in a so-called false vacuum, a meta-stable state that could spontaneously decay. Following the decay, physical constants would acquire new values and the laws of physics would all change.
How different are you gonna allow a thing to be and still call it the same thing? Would you be you if you were born in the next hospital room over? Or born in Michigan? Or in France? Of a different gender? What if you’d been born in 1645 in India? What if you’d been born a chimpanzee? A hamster? A crocodile? At which point are we talking about a thing that’s other than you?
Figure out the same conditions for identity for the universe, then ask the question again.
In current theories, there are a few dozen known free parameters in the Universe. That is to say, there are that many different numbers which are important to the theories but which, so far as we know, cannot be calculated mathematically, and can only be known by measuring them. Every so often, someone does come up with some way to calculate one of them, and the number of free parameters goes down (I think that the last time this happened was when Higgs noticed a relationship between the masses of the W and Z particles). And every so often, someone discovers a new constant (such as the mass of some newly-discovered particle), and the number of free parameters goes up.
Some physicists like to speculate that, if we could just figure out how, we could calculate all of the constants of nature, and so there would be no free parameters at all. But if this can be done, we’re nowhere close proving it, or to knowing how to do it.
So although we keep pushing back earlier and earlier into the Big Bang, we don’t yet know if things always would play out the same way from that point of time. Is there a later point of time where we do know it will play out the same way? That is, all the variables have been set by that time and things will always play out pretty much the same way from that point on? So other than the location of where all the stuff ends up, the other physical properties of the universe would be the same.