Without some form of mind control or memory alteration, it can't. The greater the number of people who are aware of a secret, the shorter the period of time that secret can successfully be kept.
David Grimes wrote an oft-cited paper in PLOS One in 2016 that developed a model to estimate how long a conspiracy could successfully operate without it being revealed, based on the number of participants involved in it. The model makes three assumptions: that any leak, intentional or accidental, blows the conspiracy, that participants are generally dedicated to keeping it quiet, and that there's no outside party actively seeking to expose it (so any exposure has to come from within the ranks of the conspirators themselves). The model used data from real conspiracies (such as the Tuskeegee Syphilis Experiment and the NSA program Snowden exposed) to make estimates as to probabilities, and then compared it to the number of people necessarily involved in popular conspiracy theories (Moon Landing Hoax, Vaccine Conspiracy, etc) to calculate how long that number of people could keep a secret.
We'll use the vaccine conspiracy as an example. It assumes that 22,000 people would be have to be in on it (namely the CDC and WHO), and they could be expected to keep it secret for maybe 35 years. Note that's 22,000 people total, over the entire timespan. However, if you included the major drug companies as being in on it, that's 714,000 people and the best you could hope for is a bit over three years.
Grimes then worked the other way: if you wanted to keep a secret known for a given length of time, with a 95% probability of it staying a secret, how many people over that period of time know about it? He only went up to 100 years, but his calculation was that the maximum number of people who could be in on the conspiracy over that time was 125. That's 125 people over that 100 year timespan, not 125 at any given time (unless all the conspirators are participants for that entire century, of course).
Given the parameters you indicated in the question, there's no way the secret can be maintained, with active participants, for the length of time you want. If the military force and government officials who do know the secret number 2,500 or more, your best case is that it lasts 5 years before the probability of it being blown starts increasing.
Grimes includes a chart for a conspiracy with 5,000 people involved. If there's only a 0.0005% chance in a given year that someone will blab or make a mistake that reveals the secret, after 30 years there's 50/50 odds it's blown, increasing to 90% after 100 years even though the conspirators may be dead or dying.
If there's a 0.005% chance someone screws up, after 20 years there's essentially 100% certainty it's revealed. If there's a 0.05% chance in any given year someone screws up, it won't last more than five years.
How confident are you that your conspirators can keep a perfect record for more than 99.9995% of the time?