It's pretty clear the way the season has been set up so far the mystery is "where is the Federation." What caused The Burn is a side issue. It's not the plot for the show, it's a necessary McGuffin that causes the setting to work.
I'm not saying that we might not find it out, but making this the primary quest of the season seems silly at this point. The trail is very, very cold at this point after all.
There is no in-universe reason as of yet to think the Federation in particular was targeted. If dilithium elsewhere in the galaxy was fine than the Dominion or the Borg (or someone else entirely) would have rolled over the area. Instead things have been low-level chaos.
Undoing The Burn doesn't actually accomplish anything. As I said, it provides all appearances of having been a one-time thing. You can't un-explode the dilithium, and you can rebuild stocks right now.
IMHO if we discover a cause, it's either going to be some sort of natural disaster which was inadvertantly caused by the Federation (as a global warming analogy) or it's some Q-like entity trying to teach us a lesson/take us down a peg. In the case of the latter there's not a damn thing that Discovery can do about it anyway.