How did Nixon get Archibald Cox fired? He fired everyone in the line of succession for the Attorney General until he found someone who would do what he asked. It is not inconceivable that the same thing could have happened with the FDA.
With the history that Trump had for firing people who did follow unreasonable orders (e.g. Rod Rosenstein), it becomes entirely plausible that he would fire any FDA head who did not support a vaccine, regardless of the science behind them. As things turned out, the studies did support the vaccine, but it was not unreasonable to draw a distinction between unbiased experts and experts under threat of firing.
With the history that Trump had for firing people who did follow unreasonable orders (e.g. Rod Rosenstein), it becomes entirely plausible that he would fire any FDA head who did not support a vaccine, regardless of the science behind them. As things turned out, the studies did support the vaccine, but it was not unreasonable to draw a distinction between unbiased experts and experts under threat of firing.