Actually, in the prime timeline, Tobin Dax was said to have met a certain Cardassian poet on Vulcan, which means we can assume the Federation had made contact with Cardassians (and the Trill, for that matter), by his lifetime (late 22nd/early 23rd century).
That doesn't necessarily follow, just because a Cardassian can travel to Vulcan, doesn't mean the Federation interacted with the Cardassia Union.
Guinan was on Earth in the late nineteenth century, but she wasn't there as a representative of her people to the local government, she was a anonymous tourist.
Dax was in Jackson, Mississippi around the year 2250, that doesn't mean the Federation had a clue who the Trill were for nearly another century.
The Nerada was also able to shrug off the explosion of the USS Kelvin ...
After the Kelvin collided with the Narada, the Klingons were able to take the Narada's crew prisoners. The Narada couldn't fight the Klingons off, and it couldn't run away. It was dead in space and helpless.
despite the Narada being a mere mining vessel, for whatever reason, she was armed to the teeth
Was it? The only armaments the Narada possessed were missiles, it had no beam weapons (iirc) and after following Spock away from Earth, the Narada ran out of missiles. At which point it was effectively disarmed. The drilling rig wasn't really a weapon.
The Narada had enough 24th century missiles to engage approximately 55 antique ships from a century before.