There are photographic special effects that help to see this.
There's the motion blur, or the frame blend, where a moving person leaves a trail.
Now combine the motion blur and the time slice. A ball becomes elongated as it moves through time.
The motion blur lets us imagine a person, let's say a woman, moving through time, adding a fourth dimension. Now think of her, in a frozen motion blur, and let's move around her and examine her from every viewpoint, in both time and space.
She walks, a blurring caterpillar.
She dances, a many limbed creature, a swirling shape. Look at her in these tiny stretches of time, viewing her as the four dimensional creature she us. We're projecting the three spatial dimensions and time onto the two dimensions we can visualise, but we can take the cross-section where we like, then move the cross-section in our mind, to try to glimpse a sense of all four dimensions.
Now take her entire life. A single creature, viewed from finish to start, slowly assembling from separate particles, rising from her final collapse to her feet, then winding back in time from that last moment of her life, a human millipede, back towards her youth, meeting and meshing with others along the way, wrapping the long skein of her life around and through objects and other lives, back until her birth, where the long, tangled spiral finally joins to its mother, linked by an umbilical cord, which shortens, taking them back into the womb, where she disappears from our view. But now her mother, her own life stretching out from this moment, can be followed back, through her umbilicus to her mother, and on the way is the intricate weaving together of the two strands that conceived the child, that made those two strands parents, and from that point we can follow the father back to his own birth and mother, and forward to his own death and dissolution, just another leaf on this tree of existence.
And the further back we follow it, the younger the species, until it is not the species we knew, and along the way we have met other branches, other primates, then further back the branching of other mammals, each of which spreads to form its own tree with thousands, millions, billions of limbs. We can find our way along these branches, towards the trunk, to the ancient seas, and in our four dimensional world, where time can be travelled in either direction, in a blink of the mind's eye, all branches simultaneously exist.
The cat on our lap, the cockroach scuttling along our floor, is joined to us, bound to us by a network that is intricate, permanent and indelible. We belong to each other. All of life is joined in this family tree.
And with each moment of time, the tree grows outward, the hyperspherical boundary of its existence expanding forever.
We find it hard to see because we don't see in the time dimension. We see with light, and light and time are inextricably linked. The processing of our minds depends on neural changes over time, further obscuring our perception of time.
The idea we have of time is constructed by superimposing frames from moments of our past. The movement detectors wired into our brains use this technique, and movement is change over time.
But if we think of time as space, we can begin to glimpse it.