There are many misconceptions about evolution presented in your original post. The theory of evolution really has nothing to do with the big bang theory. The theory of evolution doesn't even say anything about the origin of life. Evolution does not take thousands of years. It happens generation to generation. Speciation, however, takes many, many thousands, if not millions of years.

There is nothing improbable about the theory of evolution. Not only is it an excellent model of the history of life, the facts behind it have been observed. It's like stating that the theory of gravity is improbable.

I really don't know what to say to your specific example of a lizard turning into a bird. My guess, though, is that the process you described is pure speculation on your part. There is nothing to say that it happend the way you described. In general, natural selection would severely reprimand any negative changes in a species, and they would die out fairly quick. I would suspect that the same principle would apply to the lizard. It would have happend much more systematically, and the changes would be beneficial for the intermediate species. That is, of course, how it happens in general.

The big bang theory states that the universe began from a singularity. The big bang would be very much like the collapse of a star into a black hole in reverse. Also, as Lenny stated, matter can not be destroyed in our universe. Black holes that swallow mass spit it back out in the form of Hawking Radiation. This is, of course, not matter, it is energy, however energy and matter are for all practical purposes the same thing, and the relationship between them is given by Einstein's famous equation. Before the big bang, atoms did not exist. Hydrogen atoms did not begin to form until at least one second after the bang -- an eternity at that time...quite literally.

That's not really true. Einstein's theory of general relativity implies that the universe is expanding or contracting. Through observations, we have discovered that galaxies further from us are moving away faster, which implies that the universe is expanding. Since the universe has been expanding, it is easy to see that at one point the universe must have been much smaller.

There is, of course, a massive amount of other evidence to support it. Cosmic radiation, as predicted by the theory, was found by the Cosmic Background Explorer. The abundance of primordial elements is predicted by the big bang -- where practically all other reasonable models have failed. The change of the state of the universe through time can be seen by a telescope as predicted by the big bang. I, of course, can not list everything that supports the big bang theory -- that would be an enormous post, but there is enough evidence supporting it that it would be likely that any new evidence found would add to it rather than replace it. Modern science certainly does know enough about our universe to make such theories. They easily did 50 years ago.

Divine intervention has enough of its own problems -- many more than either evolution or big bang. For one, where did god come from?