Just because I have never seen, heard, smelled, tasted, or touched (the only way to gather data to prove something) a unicorn does not mean they don't exist. Apart from faith, the only thing I could logically say is, "I don't know."
To answer your question, I admit to having the faith that unicorns don't exist. But there are folks out there who have the faith they do in fact exist. How are we to really know?
I think you might be slightly misleading yourself or misunderstanding what it means to prove something. Nothing, at least within science are absolute, like I could say to you, that it is a fact and it is proven that gravity works the way it does.
But there is no way for me, to take into account that tomorrow gravity will not have changed to work complete different compared to how we know it works now. So maybe the Universe works in a way so gravity changes how it works every 14.6 billion years or how old the universe is and that just happens to be tomorrow that this shift takes place.
So when scientists talk about facts and something being proven, it will always mean within this limit and that this is based on the current data that are available to us. And if all those data from experiments, observations etc. throughout the years keep confirming a certain thing to work a given way, it is reasonable to assume that, this is how something works and that this is also how it will be tomorrow.
Therefore in the case of unicorns, where no data have been collected, in form of observations and fossils etc. then there is no basis to assume or even consider that unicorns are real and therefore the believe in unicorns being real is not equally valid to there not existing unicorns.
But again that doesn't mean that on some random planet in the Universe there ain't running unicorns around, but it is simply not valid until some sort of theory or observation have been presented for why they should exist. Someone simply believing it to be the case, is not something anyone ought to take serious.
Take something like dark matter and dark energy
(See below), we can't see it, taste it or touch it. So why is that a valid hypothesis when unicorns ain't?
The reason is due to other observations where things doesn't add up, but if something like dark matter and energy exists, it would fit what some of the scientific models predict. Which is why it makes sense for us to test and look for it. And should it turn out to be wrong, then they will have to start over, because with our current knowledge, things still doesn't add up, if dark matter and energy is not there. A lot of people have the impression that science is simply about proving what is correct, but actually its much more about figuring out what is definitely not correct.
Which is why you could make an experiment, trying to figure out what will causes paper to burn?
So first you take an ice cube and see if that works, which clearly doesn't cause paper to burn. Eventually you try to light a match and the flame make it burn. Obviously that tells you that fire from a match will cause it to burn, but that doesn't mean that nothing else will also not do it. So its very informative to know that fire can cause it to burn, but equally interesting to know that the properties of a ice cube won't.
(Clearly this is a very simple example)
But the moment we don't have an answer that is obvious, finding out what is clearly not the case, is very important.
So in regards to unicorns and whether they exists, there is no reason to look for them, and therefore it is not equally reasonable to assume that they exists as them not existing.
So, ultimately, saying that "I don't know" is correct, but from a rational point of view, it makes little sense, because you would have to relate to whatever claim people make, in discussions with no purpose to them, like me saying:
"You not believing in a planet made out of marshmallows, doesn't mean that one doesn't exists." But such statement is completely useless and meaningless, if I give you no reason to even consider whether or not one should exist in the first place, Which is why, a meteor made out of marshmallows hitting Earth could change that. But until that happen, why even bother with it?
Hope it makes sense
From wikipedia:
Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe and about a quarter of its total energy density. Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts think that dark matter is abundant in the universe and that it has had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with observable electromagnetic radiation, such as light, and so it is undetectable by existing astronomical instruments.
Primary evidence for dark matter comes from calculations showing that many galaxies would fly apart, or that they would not have formed or would not move as they do, if they did not contain a large amount of unseen matter. Other lines of evidence include observations in gravitational lensing and in the cosmic microwave background, along with astronomical observations of the observable universe's current structure, the formation and evolution of galaxies, mass location during galactic collisions, and the motion of galaxies within galaxy clusters. In the standard Lambda-CDM model of cosmology, the total mass–energy of the universe contains 5% ordinary matter and energy, 27% dark matter and 68% of an unknown form of energy known as dark energy. Thus, dark matter constitutes 85% of total mass, while dark energy plus dark matter constitute 95% of total mass–energy content.
Because dark matter has not yet been observed directly, if it exists, it must barely interact with ordinary baryonic matter and radiation, except through gravity. Most dark matter is thought to be non-baryonic in nature; it may be composed of some as-yet undiscovered subatomic particles. The primary candidate for dark matter is some new kind of elementary particle that has not yet been discovered, in particular, weakly-interacting massive particles (WIMPs). Many experiments to directly detect and study dark matter particles are being actively undertaken, but none have yet succeeded. Dark matter is classified as "cold", "warm", or "hot" according to its velocity (more precisely, its free streaming length). Current models favor a cold dark matter scenario, in which structures emerge by gradual accumulation of particles.
Although the existence of dark matter is generally accepted by the scientific community, some astrophysicists, intrigued by certain observations which do not fit the dark matter theory, argue for various modifications of the standard laws of general relativity, such as modified Newtonian dynamics, tensor–vector–scalar gravity, or entropic gravity. These models attempt to account for all observations without invoking supplemental non-baryonic matter.