The Argument from Divine Hiddenness

I've always maintained that the only atheistic argument that carries any weight whatsoever is the problem of suffering. Even if this argument were successful (and I hold that it's not), that wouldn't mean there is no God, but only that there is no maximally great God. The so-called argument from divine hiddenness (ADH) goes something like this:

1. If God exists, there would most likely be compelling evidence that he exists. (Premise)

2. There is no compelling evidence that God exists. (Premise)

3. Therefore, God most likely does not exist. (From 1 and 2)

I will grant premise (1), although there are theists who would challenge even that premise. However, premise (2) seems to be nothing more than question-begging. In order to justify (2), the proponent of the ADH would have to simultaneously refute, or otherwise undermine, each of the arguments for God's existence. In fact, the Bible states, "since the creation of the world God’s invisible qualities — his eternal power and divine nature — have been clearly seen, being understood from what has been made, so that people are without excuse" (Romans 1:20). Why think that Paul is wrong?

It turns out, then, that the ADH is really just a round about way of denying the arguments of natural theology.