God is not bound by the constraints of our universe... is that how you rationalize God (who is infinitely complex) not ever having a beginning and never being created? If you can argue that about god, why not consider something else having existed before the laws of space and time were created moments after the big bang?
OK, let's condsider that. Tell me what it was.
It really isn't a question of "rationalizing" God being eternal and uncreated. Time seems to clearly be a function of our physical universe. Anything existing outside the boundaries of the physical universe - even another universe - would logically seem not to be bound by space and time constraints. How much more so the eternal Creator who designed both space and time!
You are ignoring the even more difficult question about where God came from. I repeat that if God didn't need a creator, then why did our even simpler universe demand it? God is by definition superior and more complex than our universe which you say demands a creator.
My point is that God is, by definition, both infinite and eternal, and is the Source of all created things. It would be expected that He would be more complex than the universe He creates. Is not the designer of a house more complex than the house itself? By definition, God is a special case, there is no other like Him.
Can I prove with certainty that God exists? Of course not. But I think that the fact that billions of people have claimed to have had experience with God is a strong argument for His existence (as my textbook for Intro to Philosophy pointed out, if even one of those people was correct, then God exists). How could we ever know about such a being unless He revealed Himself to us? Yet revelation is, by its nature, subjective.
Your assertion, imho, is much more unlikely. Matter that should not exist at all, for some reason, does. Physical laws, that should not exist at all, for some reason, do. For no apparent reason, and with no particular impetus, this undifferentiated simple matter starts to arrange itself into complex structures, which develop with increasing complexity until some of them are sufficiently complex that they are able to think about what they are.
You may want to visit a junkyard sometime to determine whether matter left to itself tends to become more complex or less so.
Laws of physics cause particles to interact. Other physical laws, such as gravity, cause particles to collect and form heavier and heavier elements.
Why should these laws exist at all? If you assume that simple matter existed and that gravity acted upon it (even though there is no reason for either the matter or gravity to exist), what was the catalyst that made gravity act upon it at one point in time rather than at another? If there was such a catalyst, then you have introduced an outside force acting upon the matter. But if there was no catalyst, why did anything happen at all?
The laws of physics in our universe were created moments after the big bang, but there is no reason to conclude that before the big bang other physical laws did not exist at all.
There is also no reason to conclude that they did. There is no reason to conclude anything at all about what existed before the Big Bang - matter, no matter, energy, no energy, physical laws, no physical laws - nobody knows. You are arguing from a total vacuum. You don't have a clue where or what this universe came from, but you are willing to dismiss out of hand the possibility of intelligent design - the possibility that, in my estimation, makes the most sense, particularly in the absence of other information to the contrary.
"Why do humans seem to have this uncontrollable urge to believe in supernatural beings?"
Because that's the way God made them - with an internal urge to seek Him?