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But it also could’ve strictly been part of a covert operation to trigger it at just the right time, as part of an attack in the temporal wars.
Would doing that not have opened up just as much risk to the Romulans as to the Federation? It is a Romulan cloaking device in Federation control. If they were able to use it to time travel, they could do some serious damage to earlier Romulans before being detected. If that was a known issue, the Romulans would fit it to one of their ships, without having to involve the Defiant in all that mess.
Think about it, doesn’t it seem very convenient that Sisko and Bashir end up in this very formative period and place in Earth history?
Not really. A surprising amount of time travel, where Earth is concerned, tends to end up in and around that time. Possibly due to some spatiotemporal conditions, or simply the amount of time travel to about that era making it so that the fabric of time is weakened, and it is easier to travel to that period in that location.
Voyager also had a Captain of a Timeship end up stranded there, and cause all kinds of problems, including blowing up the solar system in a few timelines, which might been enough of an event that time travel there was made easier, or at least, there would be a greater than usual amount of time police in that era. Throw in some imprecision because it's a time travel accident, and not an intentional event, and it's not implausible someone might have slid into the 2020s when they might have normally been headed for the 1990s.
This particular instance can’t be the singular Romulan plot involving attacks in time.
There will be a great many more. We already know that there was a Time War, with people messing with time enough that the Guardian of Forever got fed up with it all, set up some tests, and left for parts unknown. If the Federation is still around, and recruiting people from other universes and timelines, it's not that much of a stretch for there to be at least one Romulan faction that might also have a part in the Time War.
Maybe there was a Romulan Galactic Empire that sought to spread its influence to other timelines.