Readfile is best solution to download external files?

Question

I need to get a remote file and give it to user without saving it to my server disk (for hiding original URL) and found a lot of posts about download external files with various functions like file_get_contents or readfile. Already I'm using this one:

function startDownload($url){
        
    if($this->url_exists($url))

    {
        //get filename from url
        $name=$this->getFileName($url);
        
        //first flush clear almost output
        ob_end_flush();
        
        //final clear
        ob_clean();
        
        //set  headers
        header('Content-Type: application/octet-stream');
        header("Content-Transfer-Encoding: Binary");
        header("Content-disposition: attachment; filename=\"" . $name . "\"");
        
        //send file to client;
        readfile($url);
        
        //exit command is important 
        exit;       
    }

    else JFactory::getApplication()->enqueueMessage(JText::_('URL_NOT_FOUND'), 'error');

}

And that's working but there is a problem! For a file with 200 MB size it takes ~ 10 seconds to start download in client browser. I think it's because readfile first downloads whole file to my server buffer and then give it to user. Is that right?

And is it possible to make it faster? for example download be started before fetch ended or it isn't possible technically?

In fact I don't know that this method is optimised or not. Any technical advice would be appreciated.

Note :

1. I know that this function should be changed for big files and that's not my concern now.
2. I consider to buy the external server in the same datacenter to make this download faster.
3. Target is that [File server] be separate than the file [online shop].

Answer 1

I tested curl method that mentioned by @LawrenceCherone. It worked nicely but when moved it to my project the result was the same as readfile (white screen for a few seconds).

So suspect to readfile() function. Separate my previous code to a single PHP file and result was amazing! Download starts immediately.

So I think my guess wasn't right and problem was not related to readfile function.

After a little search found a minor modification. I added below line :

while (ob_get_level()) ob_end_clean();

before the :

readfile($url);

And now download starts before whole file fetched in my server.