Food for thought

(Please pardon the cliché title line.)
Here is a matter to ponder:

Many religious people believe that a "god" created the universe. They defend this claim by arguing that, since the universe is such a complex and (specifically when considering human life) beautiful place, that it had to be created by some "higher-power".

My question is: then who or what created the "god"?

Seemingly, under this logic, so complex a thing as a "god" would also be need to be created by something. Why would it make sense that a "god" spontaneously existed but not the universe? (For, would not the "god" be necessarily more complex than the universe if he (she or it) is able to conceive of and create the universe?)