When it comes to the visualization of infinity, everyone tries to imagine the "big picture" of reality and everything in-between. Unfortunately, while that isn't a bad approach it only covers one area of it. The true grasp on infinity as a whole is a multitude of cross-relays that expand without edge at every given infinitesimal node to form a limitless everything. Just a few visualization tools to glimpse it would be through expansion, possibility, and negativity theory.
In expansion theory one looks at an aspect of substance and expands their view of it to grasp a better picture of a sense of timeless infinity. The easy example is to start with a subatomic image of the basis of matter and pan out at a faster and faster rate, which shows the fibers of matter building into atoms which leads to molecules to physical structures within the world to the next step of the greater picture of an aspect of the world. The view point continues to go outward as the world shrinks as the lesser solar system comes into play to the whole system to the various stars of the galaxy to the galaxy itself until there are many. At the point past the countless number of galaxies of the universe the outer edge appears and builds until the universe itself appears as a shrinking sphere of dark matter in a boundless plain of white nothingness until other universes appear in the same void. Finally the view pans out far enough that the limitless expanse resembles the building blocks of matter, and the cycle continues with countless new possibilities of occurrence.
Like expansion theory, possibility theory stretches the view indefinitely though not out or in, but sideways, time wise, and any number of ways. Sideways perspective with infinity tends to deal with alternate realities, parallel worlds, and disjointed continuances (formed from disruptions in time) that create unlimited expanses that are beyond what is visible to current science. In the same manner, time as a quantity exists not as a line, but a sphere (for what in the larger perspective of nature isn't a sphere at its elementary value) that contains any number of possible sequences. In this way, one universe which holds one growing sphere of time can hold an endless number of possible time sequences and histories. In terms of infinity, it is hard to get more boundless in minute possibility.
Lastly, for negativity theory, the whole of reality is separated into two main parts, the positive side and the negative side which is separated by the null barrier between. This null barrier is also the void in which the various universes are held. Whenever one universe 'dies' and reverts to a concentrated collection of the most basic until of everything per unit time, it nears the point of 'null saturation'- which is the needed circumstance for a breach in the null barrier. After the breach in the barrier, the dead universe will disappear from this side of reality and reappear on the other side, carrying the null energies with it and restarting everything in what is commonly called the 'Big Bang' or start of the universe. However, instead of this side of reality, it will be in the void of the negative (or positive) side. Along with it will be all the other universes and the endless possibilities of infinity on the other side.