The Burn was only somewhere a little over 100 years ago, so they had around 900 years of advancement prior to that. But maybe we're missing more in the big picture - maybe dilithium isn't the only resource that was running short.
I don't think we need to make that assumption.
Imagine that 100 years ago, there was, for almost all intents and purposes, a complete collapse of interstellar travel. That combines with a collapse of interstellar trade and economy. If it wasn't physically on a planet (so, like, say, shipyards) it was probably lost in the Burn.
Some of what we've been presented with suggests quite incredible collapses in communication and trade, even given the difficulty of warp travel. The situation that occurred in the last episode arose because Earth had lost communication with a research outpost on Titan - that's not even beyond our own solar system, and they still couldn't maintain useful links.
Yeah. That... isn't actually terribly plausible. You can communicate with Titan by basic radio, for cryin' out loud. And they still have ships with torpedoes and phasers. They could communicate if they wanted to - they just didnt' want to, until they were shamed into entering discussion.