I think DOGE does exist, it just is a non-government entity advising the incoming administration with a deceptive name that makes it sound like a government agency rather than a privileged private lobbying group.
Most of them aren't named like government entities, given a verified-government-entity greycheck on Twitter, have their leadership announced by the incoming President elect, recruit on the explicit premise of being part of Administration policy, and have public confusion as to whether they are a government department or something else.
You’ve listed indicators that suggests it has a higher probability of becoming a formalized office of some kind, higher likelihood that key decision makers truly believe in establishing it, etc.
