With the outbreak many major vaccine companies raced to develop a vaccine that would have minimal side effects with maximum protection. However, due to the crazy circumstances, the process that normially takes years only took one. The reason for this is that before the virus can be released, two major steps have to be completed, animal testing and clinical trials. Usually in these steps, it ends with a phase where the FDA reviews how it went and a two year extended watch on symptoms. Instead of watching the entire 2 years, only the first couple monthes where observed. The clinical trial patients will still be observed for future symptoms, but at the same time with the vaccine being administered. The FDA instead of checking things at the end, followed along with the trials and gave approval as the trials went.
Learn more at: https://www.pfizer.com/health/coronavirus