The main bottleneck is getting a bunch of volunteers, vaccinating them, and seeing how many get the disease over the next few months. Kinda hard to speed that up, unless you're confident/desperate enough to just skip testing. Maybe if the disease were 10X more dangerous and you had a vaccine that was just a minor variation of a previous one, it'd be worth it.

A little time could maybe be shaved off by speeding up production. The mRNA vaccines have an advantage here, you can basically use an RNA printer to churn out whatever RNA sequence you need.