Suppose person X lacks the concept nothing. Suppose, now, whether it would be possible for them to know they exist. By that I mean whether they know they, as a subject, exist. For to make the claim that "I exist" requires the concept of existence. But I would argue this claim is untenable given that the person I am talking about does not have a concept of nothing. And to have a concept of existence - whether we are talking about things existing external to ourselves or merely the existence of our subjective experiences - requires that we have a concept of nothing.
Take the following analogy. Suppose person X lives in a universe with no light thereby having no visual experience. Suppose, also, that cannot conceptualize light. Now, concepts derive their importance based on their meaning, and for a concept to be meaningful it must be distinct from other concepts. That is, the concept must be distinguishable from other concepts in terms of their meaning. So, when I want to explain the concept of an apple I say it is round, green and so on. That is equal to saying "it is not any shape or color that is not round or green". Therefore, a concept's meaning is achieved by stating it in terms of what it is not. If person X lives in a universe with no light and cannot have a concept of light, then it seems to me that person X would not have a concept for darkness, since to have a concept of darkness would require that it be stated in terms of what it is not which is light.
Returning to the initial idea of whether person X would know he or she exists if they did not have a concept of nothing, I am tempted to think they would have no concept of existence and wouldn't think of themselves as existing.