How are you displaying the pdf? If it’s the browser default, you are out of luck. To display a pdf, after download, the browser calls the registered pdf viewer with the url. The file is fetched from the cache. This is prevent double fetch.
you can get more control if you use pdf.js, a JavaScript pdf viewer used by chrome.
and finally the format of the pdf effects display. Sometimes, data required to display the first page is at the end of the file. Remember a pdf file is a postscript program, not a data file.