It is not unusual to have to wait 2-4 months for an official job offer to come from Global Staffing after receiving the initial job offer from the hiring manager. It's unfortunate it takes so long, especially if you are unemployed at the moment!
There are a lot of factors going on in the background which you can't see, but don't worry, unless word of a hiring freeze comes down from higher up the food chain, (not likely at any time in the foreseeable future), your paperwork is slowly making it's way across all of the desks of those who have to review and approve hiring decisions.
In the interim, call or send a short, to the point email along the lines of "Hi, I'm just checking in to see if you've heard anything?" to your Boeing contact. If anything goes awry, they are likely to be the first to know. Otherwise, just try to be patient, the offer is coming.