When we are born and begin to develop in the world, we possess an intuitive philosophical position called naive realism which is committed to the idea that any product of our senses is real, be they tables, forces, time, or space. From WP:
In philosophy of perception and epistemology, naïve realism (also known as direct realism, perceptual realism, or common sense realism) is the idea that the senses provide us with direct awareness of objects as they really are. When referred to as direct realism, naïve realism is often contrasted with indirect realism.
As we get older and go about our critical thinking, we discover that our senses are not always reliable. We confabulate and fall prey to illusions, or we begin to ask questions like 'what exactly are space and time?' So, we embark in the direction of the metaphysician and begin to explore what is real and what is not, which typically the provenance of ontology. We may also begin to read the works of famous philosophers, such as Aristotle, Leibniz, or Kant to advance our thinking. The question you ask is today often discussed in the philosophy of science, since space and time are of primary interest to physicists and philosophers of physics. Often times, physicists who are conceptually specialized technicians, presume their views, or the views of their research community are solutions to such questions, but while physics may inform philosophy, it does not replace it.
Whether or not space is real will bring you to a debate between scientific realism and instrumentalism. From WP:
Scientific realism is the view that the universe described by science is real regardless of how it may be interpreted... Within philosophy of science, this view is often an answer to the question "how is the success of science to be explained?" The discussion on the success of science in this context centers primarily on the status of unobservable entities apparently talked about by scientific theories. Generally, those who are scientific realists assert that one can make valid claims about unobservables (viz., that they have the same ontological status) as observables, as opposed to instrumentalism.
So, one has to start asking questions about how does one go about knowing whether space is real or what method can one show that space is real or not. This then leads into methodological and epistemological questions. Can you touch space? Can you weigh it? Does space have properties in common with bananas, dogs, and blankets? What does it mean if it doesn't?
While the philosophical canon and the exploration of the nature of space goes back to the Pre-Socratics, the modern mathematical physical definition owes a huge debt to two men in particular, Isaac Newton and Albert Einstein, the former for introducing Newtonian space, and the latter for introducing relativity. Add to the fray the views of Leibniz and Kant, and you have a robust, but highly technical discussion of what space might be both metaphysically and scientifically. The discussion of whether space is real is also complicated by the question of 'is mathematics real?' For instance, if you believe that numbers are real and have some sort of quasi-physical existence, then that colors your views on abstractions derived from them.
Many views exist on space and perception of it, and so I'll just respond to your question by giving a quick outline of nod in the direction of Immanuel Kant, whose position in transcendental idealism is that space and time are constructed by the mind. From the SEP article Kant's Views on Space and Time which quotes Kant directly:
Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally. (Ak 2: 403)
Kant, as per Kant and the Exact Sciences (GB) was involved in trying to merge Netwonian space and Leibnizian monads in his philosophy, and arrived at the conclusion that space and time are constructs of the mind. His most famous work, Critique of Pure Reason has a section entitled Transcendental Aesthetic which addresses his mature views on both space and time, and today, is defended by neo-Kantians who believe that space is not like bananas, dogs, and blankets, but comes to be because the mind constructs it. This sits comfortably with a number of philosophical traditions including nominalism (SEP), mathematical intuitionism (SEP), and embodied cognition (SEP) that center around the fact that there is nothing directly sensible about space. It cannot be touched with fingers, weighed by scales, or seen with the naked eye suggesting it is a byproduct of the mind. This, of course opens up a deep and transformative discussion about the nature of reality itself, often provoking knee-jerk reactions by some who attack the position as being equivalent to declaring that idealism is preposterous.
The point of this answer, however, is not to affirm or disconfirm space is real, but rather, to set you on the journey of finding the right words to continue a conversation that goes back to Ancient Greece. According to a recent PhilPapers survey, three quarters of philosophers consider themselves scientific realists. The question cannot truly be answered and defended until staking out a broad range of philosophical positions on diverse questions. Ultimately, if you come to the conclusion Kant is correct, then space is not fundamental, because it is constructed by the mind.