There are three ways I'm aware of to "fast track" it. One is to not do as much safety testing, which is pretty scary. The last thing we need in this country is a vaccine recall after a rash of bad reactions.
The second is to begin manufacture before the safety testing is done, on the assumption that the testing is going to come out OK. That's just a financial risk, which in this case is probably inconsequential to the larger goal.
The third way is to push computer modeling ahead of some of the traditional animal testing, which from what my biotech connections have told me, is a decade overdue, but hard to accomplish in a "business as usual" context because nobody wants to be associated with the risk.
Note: I could very well be inaccurate or incomplete in this analysis.