Every fact we attempt to prove relies on information interpreted by our brains, which it recieves as electrical impulses. Apart from this information we have no way of confirming whether the reality we perceive actually exists outside of our perceptions. Although probable, it can't be stated with absolute certainty that these electrical impulses originate from our sense organs. They could be created artificially. We have to take it on faith that reality actually exists.
René Descartes said "Je pense, donc je suis.", meaning that the fact that he was able to think and wonder about such things was proof that he exists.
It's difficult to disagree with that reasoning (otherwise we would be experiencing disagreement, and thereby proving that we exist).
So yes, there is at least one thing that you can declare as fact: I exist.
The problem is, beyond that one fact, it's not possible to prove any other. Everything else, other than our own mental processes, does not need to be a fact.
All your physical experiences and all your memories could simply be figments of your imagination. You could really be a bug-eyed-monster currently having a bad dream. Or you could be part of an experiment, with everything you think you know having been fed into your brain by a mad scientist. Or maybe you're God, and are temporarily fooling yourself into thinking you aren't the only being in existence.
Look at your fingers typing at the keyboard. You can never prove that you really have fingers, or hands, or a body. All you can know is that you believe that such things are part of reality.
You exist. That's all you can ever be sure of.
Of course, these electrical impulses can be created artificially in our nervous system, i.e. without impact from our sensors.
The corresponding thought experiment is called brain-in-a-vat, e.g.,
I assume that the group of experimentators, who succeed to implement such a difficult experiment, will have to overcome so many problems with the real world stuff, that they are the last, who doubt facts from reality.
Note. I revised my previous answer due to the discussion with Zane and Pé de Leão.
A "fact" is also a matter of interpretation, something that is fact for you may not be for fact for me, sure most facts are widely accepted but there is always disagreements.
The only facts that exist are those within my mind, my facts are the only facts, they might change with time but they remain the only existing facts.
A fact cannot exist without some form of intellect to create and interpret it as what it is, and as such you can declare something to be fact and you can share it with others, if their logic aligns with yours it may also become a fact to them.
If i interpret it to be a fact, it is fact, if you do as well it is your fact now as well.
A simple example might be this: Two men are sitting next to each other, one of the men sees a third man in front of them, the other does not.
For man #1 it is a fact that he can see the man, that is his fact. For man #2 it is a fact that there is no man in front of them and so their logic does not align.
Is man #1 hallucinating or is man #2 simply unable to see (interpret) the third man.
In this example we cannot decide weather its one or the other, the only way we consolidate something as fact is when we bring in more people to share their interpretations, if we bring in 5 more people and all of them cannot see the third man then it will be widely accepted as fact that the man does not exist, likewise if they do, then it is widely accepted as fact that the man exists.
The general belief is irrelevant, the individual belief is important, if nobody can see something but I, it is still a fact to me that that thing exists.
This is my take on the matter, a fact is a matter of perception, i hope you can understand my thoughts as they are often hard to put to words.
Belief is a conscious decision - a choice.
A fact is anything you have personally decided to believe is true.
Because there is no common accepted higher-order authority (angels, aliens, god, extra-dimensional beings, etc.) who can validate any of our choices about what is "fact", there is no absolute reality/truth (after all, reality is just an individuals collection of all things s/he has decided to consider "fact").