So if a cult were to go about taking over the world, I suggest you turn to the fictional world of comics. In the DC universe, there’s this cult called the League of Assassins. They have about 5,000-10,000 members, but managed to figure out a foolproof way to end the world. (Obviously that didn’t happen because.. superheroes).
First of all, you kidnap a group of scientists. They should be from all different areas of science, especially biology, chemistry, and technology. Maybe have one of the cult members who is good at stealth and is also a psychologist to scout for scientists that have a superiority complex, where they would do science without care of its result (i.e. the scientists who made the hydrogen bomb or the person - Alfred Nobel - who invented dynamite) and are also pretty lonely and mad scientist-ish.
Second of all, tell these scientists only the parts they need to know. Here the path splits. You can choose to go the hard way and threaten their friends and family. Or, you can brainwash them into being part of your cult, slowly recruiting them just like you recruit original cult members. Pay each a few million. That would probably be enough if your scouts chose them right. If the cult already has extremely skilled scientists, then more power to you. Tell then to develop a small disease that can kill an invasive species. Then give that disease strain to another scientist, and tell them to make it more powerful. (“It’s not working” or “There’s a stronger animal we’re trying to kill, it’s gone rogue.”
After you have your disease, make sure you have an antidote. Tell two groups of separate scientists to find an antidote, and either tell them that you’ll try it on them, or try it on some hapless prisoner this “cult” has captured. This might take some time, but…
Then choose some of the largest cities in the world. Los Angeles, New York, Chicago, Ottawa, Mexico City, Rio de Janeiro, London, Paris… these are all cities you could use. It would be easy. Have a few people let out the disease somewhere. Depending on the type, you can do it in a variety of ways. If it’s a solid, have them go to a popular buffet restaurant and discreetly drop the disease into a popular food. If it’s gas, let them gas it at a construction site or a vaping bar where the gas would be unnoticeable. If it’s a liquid, they could go to a coffee shop and pour the liquid into all the finished cups of coffee… (I’m never drinking Starbucks after this)
While this is happening, have the cult leader meet with some rich and corrupted people and tell them that you have the power to end the world. (Don’t sound like a supervillain or an insane villain though) Sell antidotes to a select amount of people, and the money you get can be used for “greater” things, like a regime or something. (I’m assuming they want to control the world).
Once the disease is released and there is worldwide panic, tell your computer scientists to hack into the global networking system and tell everyone that doomsday's coming. Depending on the goals of the cult, they can either tell people that if they join the cult, they might get an antidote, or that everyone is going to die, hurry up and panic.
And if the people in the cult want an apocalypse as in no one alive at all, then have the antidote actually be a slow acting poison (like some radioactive element) so they support your cause. And then if there are these hermits that never ever touched anyone for the past year and also has enough food to last for many years to come, either track them down or create a disease through plants that spreads like pollen and can also infect humans. Or just nuke the world after this with money from those billionaires...
And there you go, this cult just caused the end of the world. And I was having way too much fun writing this for me to be sane…