First of all, download Google Play Books on your device. You can open the Play Store and search for "Google Play Books" and simply download from there.
Then, open the Google Play Books app and go to the settings page. From the settings page, enable the option of "Enable PDF Uploading".
Then open your desired File Manager app and navigate to the folder where your downloaded EPUB is stored. Open any of the EPUB files via Google Play Books. Your selected book will get uploaded to your Google Play Books, after the upload has been finished you can open that book from Google Play Books. You can use Google Play Books to read and sync progress across devices as long as you are logged in with the same Google account.
I hope you might find this article interesting. If you further have any questions feel free to drop a comment.