Those cosmological atheists are misinterpreting mathematics.
Yes. The universe is governed by mathematics. Math is a universal language written on the fabric of space and time and it is observed and interpreted by human beings through the laws of physics, chemistry, algebra, geometry, and calculus (ect...). Mathematics in one sense is merely the manipulation of input to generate an output. In essence, this is what the universe is formed by, however, saying that all things are affected by mere probability is nothing more than a theory. While probability and randomness can typically be the catalyst for many of the starting points of many reactions in the universe, the idea of PERSPECTIVE must be considered.
Consider gas molecules. If you look in the room around you, and you could see the gas molecules, you would see seemingly random interactions between gas molecules. [Important Note: we are using this "room" as an analogy for the "known universe"] However, if the position and velocity (which is speed and in what vector) of every molecule was known, then you could predict the interactions of all of those interactions of molecules forever (using the full laws of physics...which I would bet we don't completely know...yet). Yet, this reaction is still random as the initial start was a random positioning and vectoring of each molecule.
HOWEVER, if you expand the perspective of the model, and you consider that the room was once a vacuum, and you release the gas molecules into the room from a specific point in a specific way (where you could know the starting point of each molecule and its vector) the interactions of the gas molecules are NOT random. This is because you are controlling the start.
This is why the start of the universe is so important to both the views of atheists and religious people (Christianity, Islam, Buddhism, Taoism, Hinduism, ect...). Overall, it is about belief, not science. Descartes put is best by stating the science and religion can exist in their own spheres and not interfere (don't quote me on that...go check out wikipedia descartes)
The laws of "chance" (better said..."probability") cannot be judged as accurate. You are asking "what is the probability of the laws of probability being right" and that doesn't work. Overall, phenomenally more more data about the universe is needed.
What are the evidences that would prove beyond reasonable doubts that this universe is indeed under the laws of chance?
THERE IS NO INCONCLUSIVE DATA to say so.
Or is it just an assumption of ones imagination influenced by ones belief?
Not really an assumption, but a theory that requires more data.
Should we even consider the proposal?
Sure. Why not. Theories are meant to be tested by data. However, i personally believe that probability does control all of the natural interactions, but the problem is that is hard for probability to predict the interactions of Free Will of humans and the such. I personally believe it will be impossible to judge inconclusively wether the laws of probability "control" all of the interactions between life. Probability can go both ways.
NOTE: While I believe that all natural occurrences (physics, chemistry, biology ect.) occur by probabilty, that doesn't believe I don't believe in God. I am a Christian, but an educated one. The point is...who started the party? And that's where God comes in.
Me in my education (college degree)...not much more direct references so feel free to argue...