So the fine tuning argument has been used to argue for theism, or the multiverse. The argument as I understand it goes something like this:
We live in a universe with life.
The physical constants of the universe if even slightly different would give us a universe without life.
The existing configuration of constants is extremely improbable.
Universe is designed, or we live in a multiverse (where all configurations of constants are manifested in different universes).
An objection to this argument that comes to mind is with regards to 3. I see no reason to believe any other configuration of constants is possible. So there's an "illusion" of a space of possibilities where the laws of physics have the same equations but the constants can take on varying values. But we have no reason to think such a space of possibilities exists. We only knowledge of one universe with these specific numerical values for the constants. The probability of this configuration of constants may very well be 1. There's no way to know. So the question really boils down to, "why is the universe the way it is?".
What are the responses to this objection?
EDIT: Here's a video from a physicist that illustrates this objection: