Sounds like the problem is with your definition of miracle. "An occurrence which is so unlikely that only the intervention of the divine can explain it." A thing isn't inexplicable by the mundane because of its probability, but because it violates natural laws. And something being truly impossible doesn't necessarily imply the existence of divinity, but moreso suggests that the fault lies in your conception of natural laws.

The more common definition of miracle is "a surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divine agency." For example, if an angel appears out of nowhere before you with a message from the Lord, that teleportation is not scientifically explicable. When you open the can of worms that things can break natural laws, you can always come up with an explanation that denies the divine, like that the "angel" is actually a telepathic shapeshifting alien that can teleport and wants to scam you, but that's not the point. The point is that it's considered to be a divine act, and it's considered as such because divine is the word we have for higher powers that are unable to be explained by any level of science.

Also, once the can of worms is open, you no longer get to claim that God's existence has an infinitely small likelihood, and you have to consider whether your alternate explanation is really more likely than the explanation that all the signs are pointing to. Frankly, I don't think you get to claim it's infinitely small in the first place, as whether God is likely to exist is an unsettled debate, but it's not an unreasonable stance to hold.