Numerous companies have been working flat out since early this year on developing a range of vaccines, not just one, and it's been clear for months to everyone, imcluding dare I say the POTUS, that there would probably - probably - be news on this front from some or all of them by the end of the year.
But as we know many of the votes in the US election were cast, perfectly legally, well in advance of the actual Election Day of November 3rd - about 67% of the votes were cast early it seems (although some states wouldn't allow them to be counted, or even prepared on an administrative basis for counting, until well after Election Day...but that's another story...). On hat basis for the timing of the Pfizer announcement (or indeed any of the other announcements) to have had any real impact it would have had to be made much, much earlier in the US election process.
So I think for that reason as well as many of the others posted above (eg competition to be first to announce, need to inform financial regulators of info which may have a big impact on their stock price etc), the timing was just coincidental.
It could have happened a few days earlier maybe, but not weeks (probably) and from Trump's point of view that's unfortunate as he couldn't make the political capital out of it that he would have liked - but unless it had come much earlier wouldn't have changed anything anyway...imho