There are literally hundreds of thousands to millions of recordings of microwave background radiation observations from ground-based radio telescopes that establish the temperature of the cosmic background radiation. Anyone can examine them by requesting them from the people who recorded them (Bell Labs, NASA, Jodrell Bank, Arecibo, etc.).
There are hundreds of thousands of images from WMAP and COBE and other space observatories that map the anisotropy (or lack thereof) of the cosmic background to a fraction of a degree of arc, and you can examine those any time you want (see NASA, ESA, etc.).
There are glass plates, film images, and digital images of hundreds of thousands to millions of galaxies, with spectrographic red-shift data as well, at universities, observatories, and libraries all over the world, dating back almost 100 years. You can examine those any time you want to (start with the Mt. Wilson observatory, CalTech, STSI, NASA, etc.).
Georges LeMaitre's original paper on the expansion of the universe, with its solutions to Einstein's relativity equations showing a non-static universe, is available on-line. Go ahead and read it, and you can verify his math.
Then there are the hundreds of thousands of scientific papers from LeMaitre, Einstein, Hubble, Zwicky, Hawking, Williams, Sagan, and thousands of others detailing the evidence, reporting observations, giving the results of experiments, etc. Most are available free, but for some you'll have to buy back-issues of scientific journals in which they were published.
All of the above provide extensive evidence supporting the "big bang" theory. If you start now, assuming you have a good base education in physics, mathematics, astronomy, stellar mechanics, relativity, etc. you should be able to get through it all in, oh, 30 years or so if you do nothing else.
Go right ahead.
And if you're not willing to actually do that and look at the extensive evidence that exists, then you have no credibility being a critic of it. Your own laziness and unwillingness to actually examine the evidence is not "proof" that there is none or that it's wrong.
Peace.