Well, yes, you can write it like that, taking advantage of the conventions that allow you to have a first-person narrator who is telling the story to no particular audience for no particular motive, but even there you have to pay the price that your POV character will therefore be characterized as the sort of person who would describe things like a third-person limited narrative.
But you can equally start your story
Your Majestic Serenity.
I take pen in hand at the order of your governor, His High Serenity the prince, in order that you may learn of the high matters of state that were revealed by certain occurrences involving your humble subject, myself.
I will add that having the first-person narrator lie or withhold information without some hint that the narrator is telling the story to someone for a reason just comes across as clumsy bungling.
More importantly, a first-person narrator concentrates attention on the voice of the speaker.
On one hand, this allows you to info dump without much issue -- "I was the third daughter of a professional letter-writer in the city of Goldforest." Provided that it would be in character. In particular, if you do have, or hint at, an audience for, or a motive to, telling the story, info-dump would be aimed at that audience, for that motive. The narrator in the opening I give there might recount the practice of fairs at which professional letter-writers work as too humble for the Emperor to know, but not recount the royal family's family tree. There's a nice bit in Operation Chaos, where the narrator asks for patience if the listener already knows who won World War II (because he doesn't know who he actually is) and then starts to talk about a battle, and you learn you don't even know who FOUGHT World War II.
On the other hand, it does matter whether the voice is engaging more than in a third-person. There are characters who are simply too tedious to listen to even if their stories are interesting and would work in third person.
And a grave question is whether this character can reveal the information needed for the reader to understand. (It can, of course, be subtly slipped in without the narrator realizing it, if the author is really, really, really good. It's tricky.)
This goes all the way up to the philosophy and theme and is, in fact, most serious there. A Connecticut Yankee in King Arthur's Court is supposed to satirize chivalry. I've never heard, or read, anyone talking of it who thought it did so effectively, and a big element is the Yankee himself. Effective satire would have required an intelligent and sensitive main character, or a blundering blockhead who started out with rosy dreams of chivalry, either of whom we could have trusted to report what was there accurately -- the first because he has judgement, and the second because it was against his interest. The hard-headed Yankee is also the hard-hearted and insensitive clod who would probably have jeered if he had landed in the most exquisitely perfect Camelot because he appreciates neither courtesy nor delicacy.
And again, in Nine Princes In Amber and the other Corwin books, the story is weakened because the family treats all of reality and all the people in it as playthings. Suffering and death of "shadows" mean nothing to them. This means that even though the scale is literally cosmic and the consequences will be the entire universe, the point of view character gives us no chance to feel it. It undercuts the scale of the story.