Proving the existence of a GM is not possible, unless that's what the GM wants.
The cult can, however, make it somewhat plausible that a GM exists. The thing with GMs is, they may have the power of gods, but they still have the personality of a human. I invite you to look around on the internet for GM horror stories. There are plenty about, for example, powerplayers that drive the GM crazy, players that keep bending the rules, players that enrage a GM by doing stupid things, and there plenty about horrible GMs doing similar things as well. Bottomline is, as a player, it is fairly easy to trigger a GM response.
A player could try some of the following:
* Ask the GM for a minor favor. Players often forget to buy basic gear, such as camping supplies and reagents for magic spells. More often than not, those supplies magically appear in the player's inventory as soon as they are remembered. This method usually fails while adventuring. Better try this while in town.
* Voice corrections for the inconsistencies in the observable world. World's governed by creatures with merely human intellect are imperfect, and even if they are not, a GM may be tricked into thinking that the world is inconsistent and subsequently make some alterations.
* Make fun of the GMs mother. In a GMless world, nothing happens. In a world where a GM rules, just about anything could happen. The GM may decide to transform the player into a frog if he's in a good mood. He might have rocks fall down on the player (some GMs will even do this if the sky is clear). You're basically looking for signs of karma here.
* Incessantly invoke rules that are in your favor and conveniently forget those that that aren't. A.k.a. rules lawyering. 446
This requires a lot of experience, especially if any knowledge of the rules is obtained with practical experience, as opposed to rulebook's once could reference. Given enough experience though, rules lawyering has proven to be a great way to get ahead in the world. This is suprising, because the GM has the power to overrule everything. The reason that rules lawyering works, is because GMs don't want to be unfair: Once they have set a rule, they try to stick to it. Additionally, human psychology is such that they don't want to let a player down if the player is expecting something that appears perfectly reasonable. Among other things, rules lawyering can be used to improve the effectiveness of skills beyond their original intention or to gain knowledge you were not supposed to have access to. Invoking rules grants the practitioner more control over the outcome than pointing out inconsistencies (see above), but does so at the risk of frustrating the GM. If a GM is pushed too much, he may become resistant to rules lawyers and invoking rules will subsequently have greatly diminished effect.
What would you do if you're an NPC and don't know any players? They are pretty rare after all. Well, you go and find plot hooks. In a GMed world, there should be plenty. The Players use them to find adventure after all. When you have found a plot hook, make sure that the area or person of interest is observed. You can expect the status quo to hold until a group of people comes along that disturbs it. It might be a coincidence, but you'll know soon enough if you have that particular group of people followed. They'll probably behave a little odd, and are inexplicable magnets to trouble. A word of warning: Follow them around long enough, and it's likely that they'll confront you or your spy, but fear not! As long as the adventures are grouped together, the consensus is probably that they won't kill you if you are good at heart.
Just by following around the players you'll find plenty of support for your theory. Just remember that you'll never find any actual evidence. 446