Antimatter fuel requires highly advanced economy with advanced manufacturing technologies, and can likely only be done safely in space. These are very likely abilities that would have fallen out of reach for the Bajorans under Cardassian occupation.
I guess a lot would depend on whether antimatter power would be limited to warp spacecraft or common in wristwatches. In the Federation, the latter appears more likely... A newcomer to warp business might have its infrastructure built differently. But would Bajorans be newcomers or veterans?
Gasoline was scarce in countries occupied during WWII, but cars still kept running; scarcity was also to be found in the countries doing the occupying, and while there were steps taken to alleviate the dependence on gasoline, these were partial at best. Electricity never went out of fashion, either, in those places that had adopted it before the war. If antimatter was a big part of the Bajoran life before the occupation, it might remain that during it, too - even if there were brown-outs ("Necessary Evil" indicates there weren't any during the occupation, only after it).
Hard to tell one way or another. Antimatter isn't an energy source, it's another artificial means of energy storage, so DS9 itself relying on fusion doesn't tell us much, apart from the Cardassians having built it to be close to self-sufficient rather than dependent on fuel expensively produced elsewhere. Somehow DS9 produces or acquires enough antimatter to support runabout and photon torpedo operations, though; similar assemblies planetside might be available to the Bajorans.
Since the Cardassians strip mined Bajor's resources, any dilithium in the Bajoran system would have been high on the list of what to loot.
Which makes it curious that we never hear of dilithium being mined there. Or of Cardassians making use of dilithium, for that matter. But the subject matter is one of omissions in general - we know very little about the power infrastructure or mining arrangements of the Federation, too.
Might be dilithium is common. Might be dilithium is common in the star systems of warp-capable cultures, being the decisive factor in which cultures get warp. Might be dilithium is extra rare, but many civilizations achieve warp without it. We don't know if Sol has any, say, yet Cochrane flew.
After the Cardassians left, the Bajorans began to rebuild their economy.
I'm not sure this would be a good description of what would happen. Resources strip-mined would remain strip-mined: they could never be rebuilt. OTOH, Bajoran economy might actually be in pretty good order at the end of the occupation, as Cardassia would have wanted it stable through their occupation, and the occupation wasn't intended to end quite yet when they suddenly were forced to withdraw. The sudden withdrawal in turn wouldn't result in much additional destruction - witness the half-hearted job the Cardassians did at Terok Nor, scuttling next to nothing because they expected to be back in a week anyway.
If anything, Bajor would find it richer immediately after the occupation than during it, what with leftover Cardassian equipment now free for nationalization. We do see all the Bajoran warpship types also in Cardassian hands at one time or another - so which side stole from which?
It takes a long time to rebuild all the things you need to start producing antimatter
...Which in turn might mean the Cardassians didn't destroy those things, as they expected to return. But if the planet indeed suffers from brown-outs, as in "Necessary Evil", then there might well be problems with creating antimatter, too!
and acquiring dilithium would likely be through trade, and it was some time before Bajor had anything significant of value to offer to the wider Galaxy.
Yet there were ships coming and going in earliest DS9 already. Again one could argue that a planet being mined for valuables would be in a good position to keep on mining valuables when and especially when the overlords of the mines suddenly left...
They weren't in a position to charge heavy tariffs to every ship passing though the wormhole, but they could start collecting some dues here and there. So, they begin to resurrect their ships and gain the ability to field some warp-capable missions here and there, including runs to/from New Bajor (although the majority of logistical needs are provided by typical hired alien freighter captains), but it's a lower priority than feeding and clothing their population, after all defence is being handed for them by their Federation benefactors.
Is it, though? There are no Federation ships available to defend Bajor at any point of the early seasons. Sisko never makes Doctor-like boasts of stopping everybody who dares to threaten the place. OTOH, there's quite a bit of native Bajoran warship activity at the start of the second season, including warpship activity (or at least the three ships that invade DS9 are of the same type as the one that warped into the system at the start of "Past Prologue"). Perhaps Bajor went all North Korea and invested heavily in defense first and foremost, the power being in the hands of freshly minted resistance fighters and all? (And not the sort of fighters who'd care about feeding the people, like Shakaar, mind you.)
There have seen Bajorans in Starfleet who have graduated Starfleet academy including Ro Laren and Sito Jaxa. Learning warp theory and engineering practices is a key part of graduating Startfleet Academy. Would Starfleet prevent them from going home and using what they've learned? Questionable ethics there I think. So there are Bajorans with the knowledge. Much more likely their smashed economy didn't allow them to do anything useful, at least not for a decade or so after the occupation.
Why assume "nothing useful"? We see constant warp activity around Bajor
immediately after the occupation, often involving ship types that are closely associated with Bajor (the one from "Ensign Ro" is previously established and then makes a welcome reappearance in "A Man Alone", the one from "Past Prologue" is established right off the bat, and then "Move Along Home" gives us the final decidedly Bajoran interstellar type, even if it isn't decidedly Bajoran in that episode yet). Bajor isn't lacking in warp ability during the run of DS9 the show. Our unanswered questions only involve the time before that show - whether there was Bajoran warp during the occupation (but "Ensign Ro" showed that Orta's terrorist posse had it, until they lost it and the Cardassians framing them failed to realize they had lost it), whether there was Bajoran warp before it, and how early before it, and how Bajoran exactly...
Timo Saloniemi
They talk big, just like many of the small nation-states from over the past century that pick big names for themselves. The Romulans called it the Galactic Star Empire, but there was nothing galactic about it, and presumably all the planets they conquered had inferior capabilities - hence why they were conquered. So "no" to your point. There were plenty of other civilizations that weren't "empires" that were still on-par with the Federation in virtually every way, too.
