I have created a virtual hosts configuration and the file permissions are not inheriting correctly. I have set the permissions as follows:
Note: index.php is generated with 600 file permissions and not 775 permissions like its parent. I have attempted to delete all folders and files all the way down to var/www and re-establish permissions to ensure steps properly and the files are still being generated with 600 permissions.
EDIT > SOLUTION:
Because new files were being created via FTP, this issue was not related to the files folder permissions but rather VSFTPD's configuration and how it was assigning new files permissions generated via FTP. All the credit goes to gurcanozturk's answer on this question for the commands and pointing me in the correct direction. Below are the few steps for this specific scenario.
Open VSFTPD configuration file
sudo nano /etc/vsftpd.conf
Near the top, add (0755 being questionable)
And uncomment out