Having a high level of unprocessed materials will increase the amount that is processed each time. (cap is 2500 for all except minor metal is 1250 and precious metal is 250). So keeping your stocks up so you get the max amount each time is helpful.
Also be aware that offline and online materials are processed separately on different timers, so keep the total of each up to get the max from each. (online containers can be taken from other players FOBs). You can see the breakdown of your unprocessed resources from the resources menu.
Increasing the level of your base development team will speed up the processing timer, so add platforms to that (and on your FOB) to increase your development level.
The online resources will get processed regardless of you being online or not, but the offline resources only process while you're playing. It doesn't just work leaving your game idle, it seems you need to regularly access your iDroid or hit checkpoints to trigger the processing.