The "DOGE team" is just a group of fresh eyes and analysts that actually work with department employees for the department they are auditing. When DOGE shows up, they pick a team made of up existing members of the organization. When "DOGE has access to..." whatever system, its that departments assigned DOGE "liasons" or "task" members. These are people who have always had access to these systems. They are required to get the data for the DOGE analysts.
The media ignores this because its more sensational to say "Elon Musk now has access to all your tax information!".
I suspect the reason they are getting such big results so quickly is in the department members they are choosing to be part of their particular task force already know the ins and outs, and are already inclined to wanting to bring the fraud and waste in check but couldn't do anything until now. I imagine them as real life Ron Swansons, who finally get to be on the board for slashing the budget. For instance theres probably a database guy working at social security who's been screaming for years "hey the data has 1000 people over 200 years old. this datas fucked..." and no one wants to address it.
It is not just a handful of geniuses. Sure they might be some data and process autists helping lead some of initiatives, but most of the work is being done existing government department members, at the direction and oversite of DOGE.