First contact between the Federation and the Cardassian Union (?)

[Christopher]

From the ENT Transcript site:

TRAVIS: How do you think they'll react to what's on this planet?
REED: Well, that's what we're here to find out, but in my experience, all physical species are alike. I don't expect humans will be any different.
TRAVIS: Do you think our hosts will die tonight?
REED: It's possible. For some of the species that have come here, I've seen the whole crew die. For others, only a few.
...
TRAVIS: Oh, I don't know. They're showing concern for each other. The Cardassians did that when they were here, didn't they?
REED: Ah, but in the end they killed their infected crew, just as the Klingons did. The only difference is the time it took to reach that decision.
...
ARCHER: Trip?
TUCKER: Not exactly. I'm an Organian. a nonphysical life-form. (sits up) Trip is my host.
ARCHER: What did you do to him?
TUCKER: Nothing. We never interfere in the natural development of other species. We only observe.
ARCHER: Did you know about the silicon virus?
TUCKER: That's why we come here. To see how different species react when they encounter it.

http://www.chakoteya.net/Enterprise/87.htm

So the Cardassians had been to the same planet NX-01 was visiting. Which is still not a problem, any more than the Ferengi contact. As I said, space is huge, and it takes a long time to visit every system. It's quite possible that two different powers could visit the same planet and then not encounter each other directly for more than a century and a half thereafter.

Indeed, we know that the Cardassian Central Command rose to power as a result of a time of hardship and upheaval in their world's history. If that was, say, in the 22nd century, it could easily explain why the Cardassians were never encountered during that period; they would've been too busy with domestic crises, and perhaps economically and logistically incapable of mounting a major starflight effort.