Episode 3 will reveal that in the 30th century,
31st*
A scene from next week's episode that adds a few more details, but no cause yet
The federation was running out of dilithium even before the Burn happened. They were researching other methods of warp travel but it didn't work out. It only destroyed ships that had an active warp core. Which is why there are still ships out there, those would have been ships that were I guess in dry dock, or under construction or just shut off for whatever reason.
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