According to Kant, space is not definitely "out there." We have no way of perceiving the things as they are in themselves (the noumena), because all perception is mediated by the mind and our senses. Therefore to say that space is out there is to make an assumption that we have no way to verify. Space and time, according to Kant, are the forms of intuition, the way that our perceptions may be determined. So rather than thinking of space as something out there, it is the way our mental equipment represents the things we perceive (the phenomena):
"Thus, if I take away from our representation of a body all that the understanding thinks as belonging to it, as substance, force, divisibility, etc., and also whatever belongs to sensation, as impenetrability, hardness, colour, etc.; yet there is still something left us from this empirical intuition, namely, extension and shape. These belong to pure intuition, which exists a priori in the mind, as a mere form of sensibility, and without any real object of the senses or any sensation." (A21/B35)
"Space is nothing else than the form of all phenomena of the external sense, that is, the subjective condition of the sensibility, under which alone external intuition is possible." (A26/B41)
Kant specifically denies that space is a property or relation of things as they are in themselves:
"Space does not represent any property of objects as things in themselves, nor does it represent them in their relations to each other; in other words, space does not represent to us any determination of objects such as attaches to the objects themselves, and would remain, even though all subjective conditions of the intuition were abstracted." (A26/B41)
Secondly, a priori knowledge could in no way come from experience, not even as an inheritance from our ancestors. Otherwise, Kant's Critique would have been a total failure, because his whole purpose was to find justification for metaphysical principles such that they could be known with necessary certainty. If a priori knowledge did have its origin in experience, it could never rise above the level of contingency, because experience could at some point provide evidence to disprove it. John Locke made the mistake of thinking that he could derive such principles from experience:
"... we have to thank the celebrated Locke for having first opened the way for this inquiry. But a deduction of the pure a priori conceptions of course never can be made in this way, seeing that, in regard to their future employment, which must be entirely independent of experience, they must have a far different certificate of birth to show from that of a descent from experience." (A85/B118)
David Hume, on the other hand, didn't fall into the same error. However, even though he recognized that such principles had to originate in the understanding independently from experience, he failed to see how such principles could be applied to experience:
"David Hume perceived that, to render this possible, it was necessary that the conceptions should have an a priori origin. But as he could not explain how it was possible that conceptions which are not connected with each other in the understanding must nevertheless be thought as necessarily connected in the object..." (A93/B125)
So to answer your question specifically, there is no evolutionary argument for the problem, because it would still be rooted in the contingent uncertainty of possible experience. The most experience can do is provide us with undetermined intuitions. Concepts, on the other hand, are abstractions from raw intuitions. In order to understand Kant, it's essential to understand that intuitions don't abstract themselves. There's nothing in intuitions that suggests the possibility of concepts or knowledge. It's the difference between seeing a mix of colored paint on a canvas and seeing what the painting is depicting. It's difficult to explain, because we tend to take too much for granted. Understanding these things requires some careful reflection.
Take Descartes, for instance, when he said "I think, therefore I am." In that affirmation, he found the kind of certainty that experience can't provide, and from that he had something to build upon to develop his philosophy about the world. Kant also took the same starting point, but he went in the opposite direction. Instead of simply regarding it as foundational, he sought to understand what foundation such certainty has:
"But this representation, 'I think,' is an act of spontaneity; that is to say, it cannot be regarded as belonging to mere sensibility. I call it pure apperception, in order to distinguish it from empirical; or primitive apperception, because it is self-consciousness which, whilst it gives birth to the representation 'I think,' must necessarily be capable of accompanying all our representations." (B131)
"For the manifold representations... must conform to the condition under which alone they can exist together in a common self-consciousness, because otherwise they would not all without exception belong to me." (B131)
Notice that he's saying here that representations could not exist in a common self-consciousness, i.e., the "I think" wouldn't be possible, unless certain conditions are met. To discover those foundational conditions, he had to treat "I think" as a conclusion to be derived from principles that are even more fundamental. In other words, he was digging deeper than Descartes in order to discover the conditions that make thinking possible; when you do this, then what you find is: you can never get past the foundational elements of knowledge, such as concepts, to discover some basis in experience, as if raw intuition could themselves provide the possibility of knowledge. Multiplicity, for example, doesn't itself suggest the idea of possible unity. A whole doesn't suggest the possibility of parts. Those are abstract concepts which presuppose the ability to abstract. For that reason, Kant concluded that a priori knowledge is rooted in the understanding itself:
"[T]he concepts met with in metaphysics are not to be sought in the senses but in the very nature of the pure understanding, and that not as innate concepts but as concepts abstracted from the laws inherent in the mind (by attending to its actions on the occasion of experience), and therefore as acquired concepts. To this genus belong possibility, existence, necessity, substance, cause, etc., together with their opposites or correlates. Such concepts never enter into any sensory representations as parts, and thus they could not be abstracted from such a representation in anyway at all." (Inaugural Dissertation, sec. 8)
