The contingency argument is typically constructed as follows:
P1. If x exists, there must exist what it takes for x to exist (also known as the Principle of sufficient reason)
P2. The universe exists.
C1. Therefore, there must exist what it takes for the universe to exist.
P3. What it takes for the universe to exist cannot exist within the universe
C2. Therefore, what it takes for the universe to exist must transcend the universe.
This reasoning commits the fallacy of composition, just because things which are a property of the universe are contingent, does not mean that the universe itself is also contingent. Atheist philosopher Bertrand Russell famously contended:
I should say that the universe is just there, and that’s all. . . . I can illustrate what seems to me your fallacy. Every man who exists has a mother, and it seems to me your argument is that therefore the human race must have a mother, but obviously the human race hasn’t a mother–that’s a different logical sphere. 1