Being absolutely certain that someone has downloaded a file is not something you can do in PHP. You should need something running on the client's machine to verify that the file had been downloaded (and not corrupted in transit).
It might be possible to force the user to click a download link for the PDF before you permit them to proceed, but that doesn't sound all that much better than forcing them to set a checkbox to indicate that they accept the terms and conditions.
All that said, I'm not sure legally speaking if accepting a site's terms and conditions by clicking a checkbox is a binding contract. You might want to consult a lawyer before you go spending all kinds of time working up something complicated but pointless.