Download large PHP files?

Question

With the following code, I get a file stored in Google Drive:

$response = $service->files->get("id-do-meu-arquivo", array('alt' => 'media'));
$content = $response->getBody()->getContents();

The variable $content, now contains the file I must download, changing the headers of the page, the file can be downloaded, for example:

header("Content-type: mimeType");
header("Content-Disposition: attachment; filename = test.formato");
echo $content;

While the file is small, the above code will not be a problem, but when I need to download a large file, I get errors and etc... The page takes longer to load (much more) and then the user still has to wait for the download, making it useless. Once I intend to call such a page through a request AJAX, what are the solutions I can use? And how can I get information like how much longer for the file to finish downloading and etc..