The universe that never began and can never end is the one you see around you.
1) Infinite similarity is impossible (by definition of "infinite").
2) Every point in space affects every other point adjacent to it (by definition of "adjacency").
3) Infinite discontinuity is impossible.
Logically these premises mean that at all times what looks like empty space to us is really an ocean of subtle motion. A different state of existence logically cannot ever be and has never been. As it is impossible for existence to be in any other state, there could never have been a beginning to the only state possible.
The Quantum Magi talk about "random" creations, but it is not "random". Nothing is ever actually random. The subtle motion within every seemingly empty area of space is in the form of "affectance" or what we could measure as electromagnetic and/or gravitational waves if they were large enough to detect.
Smooth waves, rather than spiking random points, are formed due to the mutual affect of every point on its adjacent points. The waves move due to every point in every wave still affecting every adjacent point as the mutual affecting causes shifting in the wave peaks. The "splashing" around of those affectance waves creates a probability pattern concerning the strength of the waves. That pattern is what we eventually see as the beginning essence of the universe emerging, seemingly from nothingness.
As the strength of some waves increase sufficiently, they combine in collision with other waves to form a small particle wherein the affectance noise is clustered around a single point. That congestion of noise containing maximum rates of change is what causes the particle to have inertia and a field of gravity surrounding it as the congestion spreads. It becomes a "hard" particle due to the amount of congested affectance noise. We then declare it to be "matter".
Eventually, the numerous particles begin clumping as they attract each other through both gravity as well as electric potential differences. Some particles merge in such a way as to form a large single particle as their noise unites into a single spinning cluster. This aggregating forms positive, negative and neutral particles that form atoms and larger mass clusters.
Very slowly, larger masses and objects are formed. Trillions of years latter, those clusters have attracted more such clusters and form larger masses such as gas clouds, and small stones.
Eventually a very large single particle is formed that has a comparatively huge inertia and gravity. That particle begins to suck in everything around it as it forms into what we see as a "black-hole". The average black-hole is estimated to have several hundred million times more energy absorbed into it than the average star/sun and they just keep growing.
Such black-holes form at extreme distances from each other. But having extreme mass attraction and necessarily having a difference in electric potential, they have no reason to stay away from each other forever and slowly begin to converge as they still grow. What do you think happens to all of that energy once one falls into another? Even if there had never been a Big Bang, eventually there would be.
Eventually the speeding single particle black-holes collide. When some collide at perhaps not too great a speed, they absorb into each other to become merely a still larger single particle black-hole. But some collisions occur at such extreme speeds that the black hole particles explode. When that happens, they release enormous amounts of energy in the form of huge particle clumps and clusters that take the form of stars and large planets and meteors as well as a tremendous amount of radiant energy and smaller formed particles.
But still later, all of that newly formed exploding mass and energy form their own new particles as mass attraction and electric potential still keep bringing them together and forcing them to ether bond in orbits or unite into single particles. The star clusters are so energetic that the bonding cannot keep up with the releasing collision energy and thus they get into a burning cycle until enough radiant energy is released that stable atomic bonds can be sustained.
The Never End
That is how your universe got here and how the other distant universes are forming. And as this universe dissipates from its initial explosion to become extremely thin in mass density, the whole process is already reoccurring elsewhere, fore the attraction effects never really stop - ever. Every new cluster of galaxies forms in its own vast segment of space from its own Big Bang. Infinity is a very, very large place.
It is all an eternal dynamic process that never began and will never end. The larger infinite beginningless and endless universe view is that of clouds forming until rain drops fall upon the surface of an endless ocean that in turn generates more clouds. Each splash is another Big Bang and to us, an entire universe.