We run into a similar issue when trying to deploy our own CDN on cloud run and so far I have not found any work around to support downloads on the browser. Without setting a content-length header, which you cannot alongside the transfer-encoding header, the browser will have no way of knowing how big a file is and on some browsers, a file may fail to show the progress bar or even how long the download will take.

Unless you plan on doing downloads on the JS or any client, which for mobile browsers may be limited for large files, cloud run may not be the best for hosting streaming.