In AWT the relevance of Big Bang theory is closely related to the concept of "Observable universe" and the "edge of observable space-time", which depends (as everything in AWT) on duality between insintric and exsintric perspective. According to the theory of cosmic inflation and its founder, Alan Guth, the entire universe could be (at least) 1023 to 1026 times as large as the observable universe, which roughly correspond the speed of gravitational waves propagation through observable Universe.
From insintric perspective we can apply principle "Similia simillibus observatur" (only things of similar nature can interact mutually in observation) - so we can consider, Universe is composed of many different combinations of Aether states, whereas we are composed from limited number of such states, being only part of Universe. If the probability of occurrence of our particular combination of states decreases with distance, then the probability, we could interact with the rest of Universe decreases with distance as well. Therefore we can observe "edge of space", but we cannot reach it, because we would evaporate first in unfriendly ("hot") vacuum around it.
This is basically anthropocentric "black hole model" of Universe formation, which introduces evolutionary absolute reference frame: if we evolved in certain part of Universe, it's because, the conditions were relatively favorable for us here and if we would travel outside of from this pretty place, we can only face problems there. It's evident, every surface of matter, like hot star or black hole forms such natural boundary of observable Universe for us and it's even possible, matter in remote galaxies evolved into exotic forms of matter, which would annihilate (i.e. explode) less or more completely in direct contact with us.
Exsintric perspective of Universe is less real but more optimistic and it has no apparent boundary: the probability of our particular combination of states decreases, but the number of new combinations increases even faster with distance, so we can always find a some friendly combinations of states there. Until space-time is formed by "friendly combinations" of states, it means, we are observing free space, so we can travel through it without apparent limit and danger - but there's no certainty, we aren't just moving in circles during this, because concept of distance and free space is tautological here. From AWT follows, real appearance of Universe is a formed by nested foam mixture of insintric and exsintric perspective: there are many places, where we can finish in our travel prematurely (planets, stars and black holes) - but in general Universe appears as an empty free space due the Olbers paradox.
Olbers paradox is a consequence of Cosmic Microwave Background Radiation (CMBR), which is behaving like subtle density fluctuations of space (i.e. gravitational waves) violating Lorentz and Poincaré symmetry, which results in gradual dispersion of light into hidden dimensions of space-time in analogy to spreading of splash ripples at the water surface. This analogy follows directly from concept of dense Aether of AWT, but it's not completely new, as it was proposed independently by James Clifford Cranwell between years 2001 and 2007. Mr. Cranvell's concept was bright, but it illustrates clearly, without active (self)promotion no idea has chance to become famous in fast expanding Internet space, if it has no immediate usage for sufficiently large group of people - no matter how brilliant it is. Unfortunately Mr. Cranvell didn't recognize the power of dense Aether concept as such and he turned his attention to derived concept of omni-directional expansion of space-time, which is apparently more abstract and it can be interpreted in dual way by AWT.
For observer of transversal waves at water surface the speed of ripples increases fast with distance (they change into gravitational waves), which can be interpreted from the perspective of this observer as an omni-directional expansion of space-time with distance. The same situation is relevant for observation of distant parts of our Universe via light waves.
At sufficient distance from observer wavelength of transversal waves ceases to zero, which can be interpreted by this observer as an initial singularity of Big Bang theory, or like surface (event horizon) of black hole (cosmic void), which observer occurs. From AWT follows, these models may be of certain relevance from perspective of numerical models - but they're all invariant to observer localtion. We can compare this situation to observation of landscape under haze - visibility scope will be limited by dispersion of light, but it will move accordingly to actual location of observer.
Because this effect is apparently nonlinear, we can explain dark energy phenomena in the same way. From outside we can see, these ripples get more dense gradually, until they disperse completely. The same effect appears at cosmological scale like slowing the speed of light in dense environment, surrounding every source of radiation, so it can be used for explanation of cold portion of dark matter and its connection to Hubble constant as well. Whereas from perspective of insintric observer, Universe appears like we would travel through density gradient, forming event horizon of black hole (some string theorists are talking about "throat of dark brane" in this connection).
From more general view of AWT this evolution is just an illusion, which follows from insintric observational perspective inside of fractal Aether foam, because we are connecting the observation of microscopic scale with the future of Universe expansion, the past with observation of vast cosmic space. Evolution of large objects is the more slow, the larger these objects are and Universe as a whole doesn't really evolve at general scale. The only question is, whether such general perspective is achievable for human creatures by experiments, i.e. by different way then just by pure human imagination.
Nevertheless, from AWT follows, Big Bang theory would suffer by fundamental problems in near future, which are of both of practical, both philosophical (ontological) nature. Observational problem with Big Bang is, we can observe well developed and separated galaxies in the Hubble ultra-deep field, when the Universe was just 2 - 3 billions of years old. And Milky Way galaxy is more then ten billions of years old, so that these ancient galaxies have not enough time to separate and develop. This conclusion was supported by recent observation of well developed galaxies (with very low speed of star formation) in ultradeep field of refurbished Hubble telescope in contrary to standard cosmological model based on Big Bang theory, in which star formation couldn't occur during dark era of universe formation.
Ontological problem of Big Bang theory is, it brings more questions, then answers - not saying about the problem of initial singularity. It can explain red shift, but it cannot explain dark energy. And it requires inflation, which appears like ad-hoced concept from contemporary perspective, although it can be interpreted as a phase transition of Aether easily and it can be reconciled with ekpyrotic cosmology in such way. But from general perspective it seems, all these models are just plural result of dispersive nature of Aether environment. The analogy of Universe evolution with stellar and galactic evolution is just apparent, because from very general and remote perspective Universe behaves like atemporal stuff (perceived mass/energy density of Aether increases ad infinitum).