What created the big bang theory?

Hello! Thank you for your question! 
I do have to say, it is worded somewhat vaguely. Hopefully I can give you an answer that helps. 
If you meant to ask "What started the Big Bang," then well, it is a very complicated situation that we don't really know the answer for. Basically, we know that the universe started out super small, under enormous pressure and at a very high temperature. There are various theories about what chemical reactions may have caused it, but the truth is we have no way to prove any of them conclusively as of yet. 
Now, if you are asking "Who came up with the Big Bang Theory," well, that has an answer! Georges LeMaitre, a monsignor in the Catholic church, loved science very much. In particular, he enjoyed the study of physics. When reading Einstein's laws on gravitation, he developed the theory that the universe was expanding. Most people did not place much stock in this, but years later, using evidence discovered by Edwin Hubble, LeMaitre was able to prove his theory. He concluded that if the universe was expanding, it must have at one time been much smaller and came up with the theory that there had been one atom at one time that had contained all the matter in the universe. 
While LeMaitre did not name this theory the "Big Bang," others did and the name stuck! This theory also influenced physics and astronomy to work together in ways they had not before. 
http://www.pbs.org/wgbh/aso/databank/entries/dp27bi.html

https://www.space.com/31192-what-triggered-the-big-bang.html