Dimensions (space, time etc.) are considered to be a priori knowledge, but if a person is born to be senseless, how can he/she perceive a world of dimensions? Since he/she is unable to have experience, he/she only has a priori knowledge.
I actually think this is a very interesting question, though as Conifold shows, not clearly answerable as stated.
Locke, of course, is generally cited as the first to work out a philosophical empiricism, though not as "blank slate" as is usually thought. Locke was also a physician and, as it happened, doctors at the time developed the first eye operations that could cure some forms of congenital blindness.
One of these doctors, can't recall the name, was interested in Locke's highly influential theories and did some informal experiments on his patients, keeping up a correspondence with Locke. He familiarized one of his patients with cubes and balls by touch prior to surgery. Then asked if he (yes, a boy, as I recall) could identify the objects visually after surgery.
Apparently, he could not. He could not innately relate "spatialized" touch experience to "spatialized" visual experience, which Locke felt supported his empiricism. In other words, the coherence of space, as we think of it, "requires some assembly."
However, I don't have references to hand and can't recall if such experiments have been repeated or what subsequent philosophers made of them. In what you might call a reverse case, Helen Keller famously developed full adult reasoning by touch experience alone.
In light of this, pun intended, I've always wondered how deeply the assumption of vision is embedded in philosophy. Certainly it supplies the central metaphors of "speculation" and "theory" and "enlightenment." Yet Logos or Word arguably arises, first with Heraclitus, in a kind of transition between oral (sonic) and written (visual) knowledge.
Given Keller's case, it doesn't seem obvious that vision is essential to reasoning or philosophy per se, at least in a kind of thought experiment. So we could speculate that it is distorted by optical metaphors. The most famous of these is Plato's, who was, incidentally, trying to overturn the oral cultural influences of Homer, a blind poet, and various blind oracles. (This very compelling thesis is set out by Eric Havelock, Walter Ong, and others.)
I'm sure much has been written on this, probably by William James, Derrida, and others, if anyone has some titles to reference, I'd be happy to know, and these might be useful to Ether Lin as well.
Obligatory "not an answer but too long for comments".
As with much discussion, it depends on the definition. Oxford Languages defines a sense as
a faculty by which the body perceives an external stimulus
For the sake of argument let's take that and run with it.
In that case, the mind would be devoid of any thoughts concerning the external world. However, assuming the individual's body is still functioning, there would be still be much bodily interactions being mediated by the central nervous system. Hence, assuming the brain mediates a subset of those processes, it would react to some internal stimuli. Whether or not the mind can react is another question.
Also, taking into assumption that thoughts are mediated by electrical signals through neurons (and that is an open question), then, at least as far as physics is concerned, there would be some inherent subconscious compliance to those signals corresponding to dimensions of space and time within the body. Time in this case would be less familiar, and perhaps merely just an order of events.
What I can make of this is that such individual would largely only be aware of only the most subtle things and at the subconscious level. If there exists a method of quantifying the ratio of conscious to subconscious processes, then the uncertainty principle may garantee that after an indefinite period of time, some of those subconcious processes could make their way to the concious level.
No knowledge is a priority to anyone. The knowledge itself is a priori, by sole virtue of e.g. being deriveable by reason alone, or being self-sufficient (tautologies).
A priori does not mean every human is born with such knowledge, or that every human acquires all a priori knowledge, or acquires it before experience. There might also be infinitely many pieces of a priori knowledge, that no human will ever become aware of in entirety.
The state of mind if humans described in the question is not knowable, so questions about that state don't seem useful in philosophy. Instead psychology or biology might agreed some light.