I'm writing method #1 right now, though I think I'd prefer #2, since the first has got me pulling my hair out, lol. JK
Yes, #1 is definitely more challenging. I have a hard time writing what I'd consider a convincing response from the character who's just witnessed life changing events. However, if done well, I think the author can draw the reader in very effectively. Origin stories are tough, but they can really draw the reader in and get them interested in the character, since their understading of the world grows along with the protagonist.
Where I find it more challenging is when I need to explain something that the character not only doesn't know, but either doesn't know that they don't know, or they understand that they are missing knowledge, but have no idea how to acquire that knowledge.
Hmmm. Which voice are you writing in? If you're using the 3rd, you could clue in the readers, while leaving the character in the dark. This can create a sense of tension.
IE
Our illustrious hero, Bob ventured into the cave, unaware that the mysterious inscription carved in the cavern entrance was actually a message of warning in ancient Sanskrit--"Beware the giant, man-eating gopher than dwells within." Alternately, with the first person voice you can clue in the readers through the narrator's experiences. The narrator might not know what's going on, but you can always instill a sense of dramatic tension, allowing them to ascertain that they've stumbled into a bad situation unawares:
I heard something crack like a dry twig beneath my boots. I looked down, and in the dim light of my lantern I saw the grisly skeletal remains of another explorer who'd ventured into these caves. I saw his bony fingers clenched around a dusty notebook. I flipped through the pages, finding mostly dull notation about rock formations, except for the last few pages which mentioned some large, unknown animal that the deceased explorer had glimpsed stalking through these tunnels. His final entry was, "Egad! The gopher has returned! Heaven save me, the goph--" Nothing else was written after that. At that very moment, I heard a strange, shrill chittering echo through the surrounding darkness..." Of course those were ridiculous examples right off the top of my head, but maybe it'll help you hatch some ideas.
Addressing your other concern, where the MC has no idea where to get the knowledge they need...
I'd say it depends on exactly what they're going after. Libraries, google.com, strong arm techniques, or cutting a deal with the devil are all options. Did you have a specific example we could dissect?