Is the process of universe creation a chaotic system? The anthropic principle says that:

The laws of nature and parameters of the universe take on values that
  are consistent with conditions for life as we know it rather than a
  set of values that would not be consistent with life on Earth

A chaotic system is:

Complex system that shows sensitivity to initial conditions

So, let's take some constants of nature:
$$ G=6.67430(15)×10−11 m^3 kg^{-1} s^{-2}   $$
$$ e= 1.602176634×10−19 C $$
$$ c= 299 792 458 m / s $$
$$ h = 6.62607004 × 10-34 m2 kg / s $$
So, I've been thinking, the process of generation of universes ( I don't know if I should called some kind of cosmogenesis or the Big Bang) somehow selects these values, possibly in a randomly way, or maybe not
I have heard of some consequences of changing the nature values, for example:

Gravitational Constant: If lower than stars would have insufficient pressure to overcome
  Coulomb barrier to start thermonuclear fusion (i.e. stars would not
  shine). If higher, stars burn too fast, use up fuel before life has a
  chance to evolve.

Or:

Strong force coupling constant: Holds particles together in nucleus of
  atom. If weaker than multi-proton particles would not hold together,
  hydrogen would be the only element in the Universe. If stronger, all
  elements lighter than iron would be rare. Also radioactive decay would
  be less, which heats core of Earth.

Or:

Electromagnetic coupling constant: Determines strength of electromagnetic force that couples electrons to nucleus. If less, than no electrons held in orbit. If stronger, electrons will not bond with other atoms. Either way, no molecules.

This led me to question myself: 


*

*"How much you need to change the constants for those things to happen?"

*"Is it possible to create some kind of universe classification for every possible value of the nature constants?", for example, if G has a value between $G=6.67(15)×10−11 m^3 kg^{-1} s^{-2}$ and $G=6.68(15)×10−11 m^3 kg^{-1} s^{-2}$ we would have a universe type 1, like the one we live, if $G$ has a value bigger than $G=6.67(15)×10−11 m^3 kg^{-1} s^{-2}$ we would have a universe type 2, a universe where stars cannot form, etc...

*"If you don't need to change that much the constants of nature in order to have a very different universe, does it mean that this cosmogenesis process is a chaotic system (e.g: If you change a tiny bit the gravitational constant, you would change drastically the universe created )?"
 A: TL:DR - We don't really know, but no, it's (probably) not chaotic.

First, let's notice that the definition of chaos given in the question is incomplete. As Ott puts it in a Scholarpedia entry, besides sensitivity to initial conditions, chaos is characterized by a "complex orbit structure" (see also the Wikipedia entry, answers in this site such as this, among many others).
Second, in principle this question cannot be answered, because all we know about the physics of "universe creation" is at best highly speculative.
That said, let's consider the question's assumption: there is a large, available parameter space of physical constants which contains a small region that results in a universe compatible with life as we know it. Then I'd say that, even if we accept this assumption, the answer is no, this isn't chaos here.
What's missing for chaos is the complex dynamics, some sort of aperiodic behavior: by assumption, once the parameters are fixed, the end state of the system is constant, either with or without life. So at most one could speak of final state sensitivity or, more appropriately here, structural instability.
Now, if we assume further that there is a dynamics in this space of possible universes, i.e., where the physical constants are not parameters, but variables, then the interesting question (with respect to the anthropic principle) would be whether this small, life-compatible region is an attractor or not - currently it's hard to even speculate about that, but if our universe spot in the parameter space were attractive, that might negate the anthropic principle. Tangentially related to the original post would be the question of whether these varying physical constants do so chaotically - but so far we're not even convinced that they vary at all.
