It appears most unreasonable to me, to deny the astronomical improbability of our universe even allowing galaxies to develop, never mind sentient apes evolving on a planet somewhere in one of those galaxies. Had the critical density of the universe at the time of the Big Bang deviated by a factor larger than 1 part in 10^15, stars and galaxies could not have formed at all*. That we are here at all is a statistical miracle. Whether or not this signifies divine intent, is up to the individual to decide for him or herself, but to attempt to explain away the phenomenal odds against our being here, strikes me as foolish and dishonest.
*John Gribbin, In Search of the Multiverse
The problem with most 'fine tuning' arguments is that they all assume we currently have the *right constants* and the correct overall theory. I don't think anyone actually believes either.
So, even if we have the right formulation of the basic laws, there are a wide range of ways to write the constants needed in the formulas. Each variant gives a different distribution of possibilities, leading to different probabilities. So, even if we are completely correct about the laws, any chance of actually computing a probability is prevented by the lack of any preferred writing of the constants.
Next, if our laws are wrong in any detail, this could easily increase or even decrease the number of basic constants in the theory. In fact, one of the goals is to find a more basic theory to reduce the number of arbitrary constants. if this is possible, then the constants we currently work with are not independent and, again, any probability calculation based on independence will be completely wrong.
Then there is the question of whether it even makes sense to say that those constants could have other values. Without a fundamental theory, this cannot be claimed. it may be that ALL of the constants are determined by a more fundamental viewpoint. We simply do not know.
Related to this is the possibility that those constants actually vary dynamically. If this happens, it is possible that the values we see currently are equilibrium values. So it may be that *any* values at the beginning ultimately tend to the values we see right now. Again, we simply do not know. Again, without a more fundamental theory (which everyone thinks is inevitable), we simply cannot say.
More specifically, your claim about the critical density at the Big Bang has many conceptual errors within it. The critical density is just what would be required to have a 'flat' spacetime. The real issue is how the *actual* density relates to that critical density: if the actual density is too high, the universe collapses before anything interesting happens. If it is too low, the matter flies apart before galaxies can form.
But this is precisely where the inflationary scenario comes into play: no matter what the actual density early on, the inflaton encourages expansion *and* matter formation in a way that leads to a very flat spacetime with matter at the required critical density. So, while your objection *was* a real concern about the theory at one point, the problems are solved in a hypothesis that aligns well with modern particle physics as well as having support from analysis of the CMBR. In particular, the claim that the density has to be correct to within 1 part in 10^15 is no longer seen as valid.