Also, the government should be efficient but shouldn’t be required to break even or profit… it’s a public good.
Agencies generally aren't just given a big sack of money to do whatever with. It's allocated for specific types of things in specific amounts, and in particular, employee pay is separate from other things and governed mostly by a given number of employee slots rather than a specific dollar amount. The forest service couldn't save those jobs by just shifting funding from, say, vehicle purchases without much higher level approval.
It doesn't really matter though because the direction to the forest service and everyone else wasn't "reduce your budget by $Y". It was "fire all your new employees immediately". There was no opportunity for the forest service to "better manage its finances". I think giving the forest service and other agencies time and flexibility to figure out how to be more efficient based on specific domain knowledge is a fantastic idea. Even if that ultimately did lead to layoffs, at least it would be an informed decision. That's not at all what's happening, and whatever excuses proponents of this approach come up with, firing people like the woman in the article is exactly what was expected.