In literature it appears far from clear with regard to specifically what 'archetype' means and what this term is taken to mean in Jungian writings. Several ideas have been advanced to define the term in both contexts all of which are closely linked yet have not been synthesized to form a single, unequivocal definition. I was under the impression that what Jung meant by archetypes is coherent ideas or at least coherent images, E.G, the mother archetype. Such things, I maintain cannot be innate. I regarded no other concept but this one as an archetype.
If it is the case that an archetype as you suggest is not what I had in mind, but simply any content of our unconscious mind that has not yet been subjected to conscious scrutiny, than yes archetypes are inborn.
In the most technical sense, some experience is required in order for us to have some content within our unconscious mind. To a minor degree, fetuses are able to cognitively process information before being born. As a result when they are born, they have archetypes or some content in their unconscious.
In the strictest sense, no idea as archetypal, yet all ideas are ectypal as all ideas in our mind have derived from the external world. Jung would be correct to maintain that some content of our unconscious was present at our birth, yet it would be a mistake to suggest that it has originated from within and not from without. The notion of 'having derived within and not from without' is close in meaning to 'archetypal', which I find to be fundamentally mistaken for the reasons stated above.