I am thinking that there also must be arguments against God’s existence that rely solely on reason, without need of appeal to observation. What would be an example ?

I think you're looking for Nietzsche and Spinoza in western philosophy. One thing that most people fail to understand that atheism is a zero sum game, i.e. to be atheist means you must reject god and it's moral principles that comes with it. On the contrary that god and it's religion often becomes moral philosophy. Whether those moral principles are relevant is a question of time and context of the time it's presented in. Spinoza argues against these principles (in extension the rules of God as set forth by the Torah), so does Nietzsche in a more post enlightenment sense.

On the eastern side this is quite often a debate and has distinct school's of thought. Take a look at Nastika philosophy
and Buddhism in general. Both of which talks only about morality san the existence of god. (There's a bunch of ancient texts that talks about non existence of god, I don't know which part I should recommend). I would say consider Alan Watts (but with a pinch of salt, he touches on it a lot)