Is there any way to speed up processing of materials?

I've discovered one way, but it might be considered a glitch, as it involves abusing the game's checkpoint system.

Checkpoints usually reset all progress -- combat deployments, development progress, any Fulton'd individuals, etc. There are a couple of important exceptions, however.

Processed materials are yours, forever, so if, during a mission, you get the "Materials Processed" notification, (processing 1000 units of Fuel, for instance), and then reset, you won't duplicate the materials -- returning to the previous checkpoint at that point will show those 1000 units sitting in Mother Base's treasury. But! Returning to the previous checkpoint will reset the time until the next "Process Some Materials" popup.

So what you really want is to trigger a checkpoint immediately before the materials processed tick triggers, so that when you "return to checkpoint", you only need to wait 2-3 minutes, rather than the 30 minute (or however fast your base currently processes) wait you'd normally have.

I've never tried to set this up intentionally, but if you find yourself in a situation where you can exploit this, it'll burn through your unprocessed materials quite quickly!

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.