I have a very similar requirement specified here.
I need to have the user\'s browser start a download manually when $(\'a#someID\').click();
But
Using anchor tag and PHP it can be done, Check this answer
JQuery Ajax call for PDF file download
HTML
Download pdf here
PHP
I am checking for file size because if you load pdf from CDN cloudfront, you won`t get the size of document which forces the document to download in 0kb, To avoid this i am checking with this condition
if($fsize) {//checking if file size exist
header("Content-length: $fsize");
}