God and Fine-Tuning I know you said premise 3 was the most contentious, but premise 2 seems like the most contentious to me because it assumes that God has to achieve certain “purposes.” In your argument you mention the God that most theists believe in. I’m not sure if most theists actually believe in the same God, but I’ll refer to the Christian God since that is a very popular one and one that I know the most about. For at least the Christian God and most likely other gods or God that some other theists might believe in, I don’t think God would be said to have a purpose. I’m not sure what you meant by purpose, but I thought of purpose like the Google definition of purpose, which is “the reason for which something is done or created or for which something exists.” The God that at least I am thinking of would not have been created and exists necessarily. In this case, it would be possible for the world not to exist, but only if God did not want it to.
Your first premise says, “According to the FTA, if some property x was not present at the conception of the universe, then the universe would not have existed.” This doesn’t seem to affect your argument as much as the objection to premise 2; however, if I remember correctly, the FTA was saying that the universe required a very precise combination of factors to exist and be inhabitable. This precise combination of factors actually happening is supposedly extremely unlikely without God. There wasn’t just one property that had to be present for the universe to exist. The Christian God seems almost like the x in the premise, except I suppose without Him, the universe could have existed, albeit it would have been extremely unlikely. To summarize, the FTA just seems to be saying that our universe seems more likely under a being like God rather than by chance. This being can be any universe creator, including the Christian God.
Going back to objecting premise 2, maybe you meant that God could have failed to achieve something that He wanted to do. However, like I have said earlier, it can be said that the universe could not have existed, but under the FTA, that refers to an existence by chance where God does not exist. It seems to me that the FTA would allow that if God exists, He created the universe and is omnipotent, but the FTA was just trying to show whether an omnipotent God creating the universe or a universe created by chance is more probable. Since the FTA says that the universe could have not existed if it was created by chance, then I don’t think that itself entails that God could have failed because in that scenario God does not exist.