No such organization could come into existence without the intelligence agencies and governments of the world being aware.
Housing, feeding, clothing, training, and arming tens of thousands of soldiers is not a trivial task. The space, and resources required to do this would cripple some countries, never mind a nameless organization looking to remain utterly anonymous.
You would need a front under which to buy these training facilities, sign arms contracts, get permission to operate in certain countries, etc.
In other words, welcome to the Atlas Corporation. (From Call of Duty)
Private Military Contractors
Use your illicit funds (which of course you've laundered) to start a private military corporation (PMC). Your original start-up location should be some corrupt little country where few questions will be asked, however you will have to register in the US, Europe, and other places in order to operate internationally.
Buy, Hire, Train
Now that you have a legitimate reason to hire troops, buy military supplies, weapons (in quantity), etc. start doing so.
Set up training operations in different countries. Build up your facilities. Maybe publicly buy or partner up with weapons manufacturers and researchers.
Be prepared for plenty of healthy interest from various spy agencies.
Build a Front
Hire "regular" mercenaries (for US Marines, British SAS, French Commandos, etc.) as your "public image troops". Send them out on fully legitimate contracts for various governments: hunt down terrorists, protect VIP's, rescue hostages, etc.
This will build your reputation as an above-board, profitable heavy hitter, and distract attention from your true operations.
Behind the Scenes
Some of your bases of operations should be open only to those loyal to your true goals. The "regular" troops would not mingle much with your true believers, or only those who know to maintain absolute secrecy.
No one would be promoted past a certain level who does not share your views and objectives. Those to whom the secret is revealed and reject it should be killed in such a way that it all looks accidental - experimental weapon malfunction, a training exercise, a terrorist attack, etc.
Take advantage of the anti-military feelings sweeping the world. There are so many conflicts which the public is against sending more troops into - offer your services, and do a solid job. Use your shadowy powers of manipulation and intimidation to keep any negative news regarding your actions in those conflicts from leaking to the public.
The governments of the world will find it quite convenient to turn to you rather than send in their own troops to fight/die (which would fuel public opinion against them).
You can fabricate your own terrorist threats and conflicts (you invent something like ISIS), and then become "heroes" defeating them.
Of course many spy agencies will be suspicious, but I trust that you will be able to manipulate or distract them as required.
Use your massive profits to build yet more military bases, buy even more equipment, and research new and terrifying weapons.
When the governments of the world have relaxed and become unintentionally dependent on you, strike.
Launch massive terror campaigns around the globe, then convince everyone that a world-wide deployment of your elite troops will put an end to the situation.
At that point it's all over but the mass executions.