Somewhat counter-intuitively, that space is not beyond the material universe itself, but is an energetic field which is actually the foundation of all matter, but not matter. It is the most subtle of energy, somewhat comparable to the necessary inspiration of architect, before a structure is built; it is the space holding space. (There is a very similar idea lately in physics, called "Quantum Monism" which proposes there is a presently undetectable type of unified energy which somehow connects all sub-atomic particles)
Ancient wisdom suggests that transcendent space (Brahman) energetically supports the entire universal manifestation; it is an energetic footprint which also supports other subtle realities which are not measurable by ordinary human sense perception or instrumentation. It is a consciousness-based space experienced by those rare souls unfettered by material time and desire - those who are forever present in the eternal moment.
Like gravity and time, transcendent space is an invisible phenomenon noted by it's symptomatic affects which are subjectively experienced by an observer. As to how and why - it is a space and an experience naturally revealed by one's subjective evolution of consciousness.
As infrared and ultraviolet rays are the ends of a spectrum not visible to the naked eye, there is a spectrum of transcendent energy only known and seen by those whose non-material/spiritual senses have been awakened - by that same underlying and all-pervasive energy. It takes One to know one.
That space can also be found in the small universe that is one's body - by going deep into one's heart, which is the seat of consciousness. The brain may flare electrical flashes as symptoms of the workings a processing unit, but actually the eternal spark of consciousness/spirit/soul, is invisibly seated in the region of the physical heart according to sacred texts.
It is from this location that consciousness pervades the entire body; consciousness is much more subtle and far-reaching than just the electrical impulses of brain activity.
One could consider that everything is heart-based on one level or another including intelligence - but that's another discussion.
Sacred texts also mention that the Supreme All-pervasive sits with each soul, conscious of it's needs and desires, and is the Source of all individual revelation - it is from internal divine grace, that transcendent space is revealed and experienced by the individual observer.
"Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be."
Material desires create another material body eventually manifesting over time, whereas spiritual desires manifest a spiritual body beyond time's reach. So how does one distinguish between the two?
Spiritual desires provoke divine expression and spark loving reciprocation individually and in the collective. Material desires fuel a sense of disconnection, triggered by unnecessary fears fomented by a delusional ego confused by unlimited desires - desires which contain the seeds of hate when denied or found to be unsatisfying even when achieved.
If one wants to be hosted in eternity - forever in the present moment immune from the fluctuations of the material elements and time itself, one can enter transcendent space through one's heart, if one is willing to actively seek that realm. Such embodiment is the nature of spirit or divine consciousness, described in Sanskrit texts as Sat, Cit, Ananda, translated as Eternity, Knowledge, Bliss.
When the realization of Eternity, Knowledge and Bliss are fully experience within by divine grace, one is blessed by the conscious understanding of one's spiritual form and function, no longer defined by material designations which veil a higher reality.
It is said that humankind is made in the image of God - Eternity, Knowledge, and Bliss are the constituent elements which form the spiritual body after death; a form like that of the Creator.
One who seeks and finds that divine presence, aided by divine grace, is known as Jivan Mukta: one who is liberated from all misconceptions, even while residing in one's present material body.
By reaching inward where the Supreme Source waits and listens, guidance will come through various channels, directed by that same Supreme Energetic Being who is inconceivably personal, yet all-pervasive at the same time.
"Seek and ye shall find"
"When the the student is ready the teacher will appear"
Cliches perhaps - but nonetheless, very true.
Once achieving a steady state of inner awareness, one can meet all internal and external challenges from a place of higher perspective as well as appreciation for the process of one's life journey.
Seek the Soul of all souls, turn your heart to pure gold, then you'll be able to laugh at your coffin