The argument is that the universe is FT for the existance of atoms, molecules, chemistry, stars, planets etc.
OK, let's start with this.
First, what do you consider the fundamental constants to be? mass of the electron? Charge of the same? Mixing angle between neutrino favors?
Please list the ones you wish to work with. Make an argument that they are independent of each other.
Second, give and argument supporting the idea that these constants should be uniformly distributed. Alternatively, give and argument that they should be distributed in some pre-defined way.
It is only with such a notion that we can make any probabilistic assessment from the values we see today. If the constants *are* uniformly distributed, then one calculation would be made. But if they are NOT, then a calculation based in the correct distribution would be made. if this step isn't done, there is no reasonable way to proceed.
Third, Decide which aspects of the universe you wish to claim fine tuning for. Be specific (which atoms, what structure for stars, which molecules, etc). Or do you wish to argue for some general characteristics (some atom that can produce complex molecules, whether or not it is carbon, some liquid that serves as a solvent, whether or not it is H2O). Fine tuning is more supported if you can use a general property and it still turns out to be rare in your chosen distribution.
Fourth, and this is one quite hard, start from fundamental principles and determine the range of the constants on your list that give the range of values allowing for the characteristics in the last item. So, for example, clearly describe the range of values for the constants that allow for the formation of a carbon atom (or other atoms allowing for complex molecules).
Fifth, after completing the previous, use the assumed distribution to find the probability that a 'random' selection of the constants would lead to your criteria (atoms, stars, etc).
After this has been done, you have some sort of probability that a 'random' universe would have the conditions you listed. We can then assess whether that probability is high, low, or intermediate.
Of course, the question of whether an intelligence assigned the values of the constants is a completely different question. For *that*, you would have to also address the following questions;
What determines the values of the constants?
Are they under the control of some sort of intelligence?
Are there other 'universes' or, at least patches of this one, with different constants?
Are all of the values for the constants actually produced in the previous scenario? If not, why not?
Etc