This all depends on what precisely you mean by exist.
Kant distinguished between the phenomenon (all the events of the mind) and the noumenon (everything else).
He held that the noumenon is unknowable in all its details and that all we can know of it is that it
is.
I would agree with him there, as the mind, as it is experienced, does not encompass enough to explain its own existence. Hence, there must be something else 'out there' which, at least in part, produces the mind. That part which is directly responsible for the mind I call the 'noumenal brain'; a stripped down definition of brain with none of its biological implications
There are also elements of the mind which slip in and out of our awareness, we always assume them to be there when out of the pinhole gaze of our awareness, but this is somewhat assumptive. We can, however, know from this that there is a part of the mind which is not within our awareness. If you would prefer to reserve the term 'mind' for that which we are aware of then we could perhaps instead say that there is 'stuff' out there which has the potential to arrive within our awareness.
I am not, in any way, arguing that 'things as we experience them' in any manner can be demonstrated to exist 'out there'. If that's all you are trying to say, then I most certainly agree
However, there are also various other ways in which things can be classified as existing, but I tend to mix my epistomology and my ontology.
For example, a unicorn can be said to exist in a number of ways that something self-contradictory (such as the Christian God or a square triangle) cannot be said to exist.
A unicorn could be said to have potentially existed, though archeological evidence is lacking, or to potentially exist should there be a creature exactly as the myths describe living outside of our view, such as on a planet far away, or to exist purely in potentia as something which we may one day create.
This is still, however, conceptual and epistomological and, hence, within the mind with its justification reliant upon some referent being discovered, a referent which can only be found in the mind.
There is another thing I will mention though, namely the multiverse. The way I use the term 'universe' is to describe a discrete set of causally linked elements, i.e. all that part of the noumenon which we could potentially come to influence through our actions, or come to be influenced by through its events. Hence, another 'universe' is inherently something which could never be observed in any manner, even as an element of the mind, because it cannot in any manner make an impression. Hence, such other universes exist purely in potentia, never capable of falsification or verification, or as an impression within the mind. But then, perhaps, still an epistemic, and hence mental, classification of the capability we have to find referents for a concept.