Do you remember exactly what code/customization you added that caused the White Screen error? If you made an edit to your functions.php file, and there was an error/typo in the code, then it could cause the site to go down depending on the issue. If it’s just the functions file that caused it, then you could replace the file through FTP.
I always recommend editing Theme files (for any WP theme) using FTP. With FTP you’re able to Undo any mistakes or typos that cause something like this to happen. With the WP Admin it’s not always possible to go back once the White Screen appears.
If you want me to give it a try just let me know. All I would need is a temporary login for your FTP (assuming the customizations to the theme were the cause of the issue). I’d also need to know what files you edited that may have caused the issue.