Usually what happens is "they" select a judge which will rule in their favor. It's that simple and has been done for many years to buy time, do damage control and so on.
I don't think that can be done at the federal level. You are in one of the 9 federal districts, you file your case. you get whichever judge is working that circuit at that time. Yes you might expect them to be liberally biased in DC or in the 9th circuit. But if your case had venue there that's where you'd be.
Someone who knows federal case might weigh in on this.