When we think about what tasks bright young people can become good at, I think auditing flows of money is one of them. It's a technical task with objective results, and a tight feedback cycle. The places where you need age and experience are like resolving interpersonal conflict, balancing interests from many stakeholders, setting up objectives for others to follow, etc.

So to me this argument sounds the same as "how can young kids think they can program like experienced engineers".

Another answer is that financial auditors don't have ALL the technical skill for this scope of project. Light SQL skills tend to be the upper end of technical accounting (many workers on a project is good for corporate billing). Reports indicate Doge is employing graph analysis, LLMs, etc. Getting the data looks like a SW problem perfect for young people. I have no evidence that this how the organization functions, but I can imagine them as technical analysts, who simply pass information to higher ups who do have organizational experience.