Remove index.php from URL Apache 2.4
If you must avoid using .htaccess, another directive you could try if you're having trouble with mod_rewrite is to use the ErrorDocument directive such as the following:
ErrorDocument 404 /index.php
If you go that route, you may need to tweak the application code slightly - like at the top of the index.php file, you might need to set $_SERVER['PATH_INFO'] to $_SERVER['REQUEST_URI']. Compare the $_SERVER contents between dev and production to get a better idea if that doesn't do it.
If you can edit the conf file as you noted, and if it's not a policy / security issue to use .htaccess, you could always enable .htaccess for the site by using the AllowOverride directive in the conf file.