Looking for a word to describe a very specific feeling of realised expectation
A literal fit would be hindsight bias (wikipedia).
Hindsight bias, also known as the knew-it-all-along effect or creeping determinism, is the inclination, after an event has occurred, to see the event as having been predictable, despite there having been little or no objective basis for predicting it.
It's also sometimes phrased as "Hindsight is 20/20," referring to the standard measurement of "perfect" human vision. It's a noun, so it fits your second example smoothly.
Jane experienced a feeling of hindsight bias when she finally completed the puzzle. Of course it was so blatantly obvious she realized she knew how to solve it all along.
I admit this answer is a bit cheeky, because you're looking for something that means they literally knew it all along, whereas hindsight bias is actually saying they didn't know it, only think they should have known it after the fact. As a counterpoint, I offer this: if Jane really knew the solution to the puzzle, why didn't she get it immediately? Or, if you really know this word exists, why did you have to ask the question?
My real point is that human memory is fallible. Just because you think a thing doesn't make it so. It's a fascinating article; I suggest reading the whole thing before you decide any understanding is inevitable. Consider this snippet:
Research shows that people still exhibit the bias even when they are informed about it. Researchers attempts to decrease the bias in participants has failed, leading one to think that hindsight bias has an automatic source in cognitive reconstruction. This supports the Causal Model Theory and the use of sense-making to understand event outcomes. The only observable way to decrease hindsight bias in testing is to have the participant think about how alternative hypotheses could be correct. This makes the participant doubt correct hypothesis and report that they would not have chosen it. However, this only decreases the hindsight bias, and there is not a solution to eliminate it.
For a real word that fits your expectations (or at least, what I think your expectations are), consider inevitable/inevitability:
adjective
1. unable to be avoided, evaded, or escaped; certain; necessary: an inevitable conclusion. 2. sure to occur, happen, or come; unalterable:
noun
3. that which is unavoidable.
Source: inevitable. (n.d.). Dictionary.com Unabridged. Retrieved July 13, 2015, from Dictionary.com website: http://dictionary.reference.com/browse/inevitable
Jane experienced a feeling of inevitability when she finally completed the puzzle. Of course it was so blatantly obvious she realized she knew how to solve it all along.
"Jane felt stupid when she finally completed the puzzle. Of course it was so blatantly obvious she realised she knew how to solve it all along"
That's how I'd feel anyway.
A lot of great minds feel like an idiot when they finally figure out something that they should have a long time ago.
The most striking example I can think of is Hercule Poirot's refrain: "I am/have been an imbecile". He says that quite frequently in Agatha Christie's books, whenever some explanation finally dawns on him.
For example, here in 'The Big Four'
"But I have been an imbecile. I see clearly at last. It is undoubtedly the blessed saints who stopped the train.
There's a thin line between this situation, and the fallacy of retrospective determinism (When someone says after the fact: "I knew all along this would happen")
When it is assumed that, because some event has occurred, its occurrence was inevitable, and should have been clear from the “obvious” causes. (Logfall.Wordpress.com)
Serendipity, perhaps ...
http://dictionary.reference.com/browse/serendipity
noun
- an aptitude for making desirable discoveries by accident.
- good fortune; luck