There a couple ways to silently install Firefox. First, you'll want to get your free download of PDQ Deploy and do the initial set up. There is a more in-depth explanation on how to build your own deployment packages here.
To create the package you will go to
File>New Package. Name your Firefox package. In the Install step click the ellipsis button in the Install File and navigate to the Firefox Setup xx.exe file.
At this point you have two options to do a silently install Firefox. In the parameters field you can type
or use an INI file. Copy and paste the following into a text file and save as a .INI in the same directory as your Firefox setup exe.
Then in the parameters field enter:
/INI=<full path to the INI>\Firefox.ini
In the Additional Files field add the Firefox.ini file. (You could also just check the Include Entire Directory checkbox but if you do this you want to make sure there aren't unnecessary files in the directory such as earlier Firefox Setup executables)
Now you're all set to deploy your silent install. Now, the easier way to do this of course is to deploy it from the package in the Package Library that silently installs Mozilla Firefox that is available with either a PDQ Deploy Pro mode or Enterprise mode license. Easier yet, with Enterprise mode you can set up Firefox to automatically deploy whenever a new version is released.
Note: Do not use /S (a common silent install parameter) because /S for Firefox performs a silent uninstall.