The hiring process in the Fed is sometimes down right ridiculous (as you mentioned, took months to apply then 30 minutes for the actual offer). I have received similar blind offer in the past too. I had to tell the HR person I can't accept/decline until I have a chance to meet with the hiring supervisor. Luckily, I am local so I called up the sup and requested a direct meeting (it's ironic that I had to ask for an interview). There is no way I would accept a job until I have a chance to meet (and evaluate) with the person (and the team) that I will work for. It's a two-way street...
Regarding your offer, will they pay for relocation? If I were you, if possible, I would come to the area and check out the office/team prior to making your decision. Good luck.