Addressing possible objections
"But a skeptic shouldn't be expecting a sign from God to make him believe. That's putting God to the test. Instead, the skeptic already has everything he needs to believe, so he should simply choose to believe".
The idea that one can simply "choose to believe" something arbitrarily and immediately is known in philosophy as direct doxastic voluntarism, and is a very, very controversial position to hold (source). It's even controversial among Christians (source). Personally, I'm strongly persuaded that it is plainly false. A simple confirmatory experiment: try to choose to believe right now that there is a teapot orbiting the Sun between the Earth and Mars. Believe this sincerely, at this very moment, without any doubts. I just can't. Instead, the perspective that generally garners more consensus is indirect doxastic voluntarism, suggesting that our control over our beliefs is only indirect. We can do so by choosing to take actions that may have an impact on what we believe in the long run, such as conducting investigation, weighing arguments and counter-arguments, and evaluating evidence. If indirect doxastic voluntarism is true (which is the view I hold), then a skeptic would only be able to attain the belief that God exists rationally through indirect means, over a period of time, for example, by engaging with arguments and evidence for/against God's existence and concluding rationally that the case for God's existence is stronger. However, this circles back to my earlier point about the complex and longstanding debates between theists and non-theists, in which it's highly improbable that a consensus will be reached in the near future.
Additionally, there is no reason to interpret the skeptic's request as the expectation of a physical sign, such as expecting that God will make a chair levitate to demonstrate the supernatural is real. Rather, God could very well answer the prayer in other ways, such as by granting the skeptic a stronger experience of the light of faith (if I may borrow terminology from Aquinas (source)).