The big bang is both testable and observable. The various by-products of the big bang began expanding outward from the emanating point at a massive but stable rate. Since their speed and direction is measurable using the Doppler effect, we originally hypothesized that the universe must be expanding. The Tolman test later confirmed their hytpothesys. This became a test and proof of the expansion theory. By identifying certain elements in other galaxies, we've noticed that the further away from the center these galaxy's get, the younger they appear.
As for the "energy cannot be created or destroyed paradox" or Newton laws of thermodynamics it is suggested in the theory that the big bang created the laws of physics. In other words, the four forces of nature (Gravity, Strong Nuclear, Weak Nuclear, and electromagnetic) were created by the big bang and didn't exist until. We are talking about energies to the power of infinity, so it doesn't seem like a stretch to say that that amount of energy could reorganize the parts of an atom.
Either way, This proof doesn't work... "If time is infinite and this ball of matter existed at a point in time, it can be assumed that the ball of matter was 'at rest' for an infinite period of time before it exploded." It really only says assume the object was "at rest" for an infinite amount of time.
What was the outside force? Perhaps it was a previous universe contracting to the critical point where its own laws of nature became null causing the big bang.
As for Faith... You cannot have faith in something that can be or has been proven. You can say you have faith in it, but it is not faith by definition.







