Applied at US Army Corps of Engineers for Realty Specialist

I recently interviewed for a Realty Specialist position with the US Army Corps of Engineers (USACE) in Seattle. The interview was this past Tuesday, and I'm still waiting to hear back about whether I've been selected. I understand that the federal hiring process can be slow, possibly taking 3-4 months before a start date, if I even receive an offer. In the meantime, I've received a job offer from a private sector company in Florida, which requires me to make a decision in about three weeks. This role involves flying out for a shadowing experience and a final interview, with a potential start date in late September. My ultimate goal is to work in the government, and the position with USACE seems like a great opportunity to get my foot in the door, especially with the fellows program they offer. I'm torn between accepting the private sector job now or holding out for the federal position. If I do take the private sector job and later receive an offer from USACE, is it acceptable to resign from the private job? I want to ensure I don't burn any bridges or jeopardize my chances with the federal job. Has anyone been in a similar situation? How did it turn out for you?