We used to think the physical universe just happened to exist this way accidentally also, and by a few simple physical laws
We know better now...
...millions of significant design improvements appeared spontaneously through lucky mutations? Not technically impossible I suppose, but I wouldn't bet on it!
Who is this "we" who "know better now?
Based on physics, chemistry, etc., the physical universe exists and operates through a relative handful of physical "laws," such as gravity, electromagnetics, quantum mechanics, conservation of matter and energy, and a handful of other forces/processes we've identified. "Used to think" and still do think, because that is what the evidence shows. In fact, there are just six numbers, six "constants," that define any and all of the material phenomena we can detect and observe in the universe.
As for your "millions of significant design improvements:" Your idea that because God created time along with space, therefore everything--including modern humans--were created all at once is nonsense. Time keeps everything from happening at once--so for humans to happen, millions of adaptations had to happen
over a period of time.
Therefore, God did not create us just as we are at the beginning of the universe...unless your argument is that God also created the original and all the intermediary lifeforms at the same moment, and all we are doing is living out an entirely predetermined existence, without choice or free will.
"Lucky mutations?" Perhaps, in a sense. Mutations are random, adaptations occur based on several different selective pressures, and there is no goal for life except (in a very different sense) its continued existence and adaptation. But to assume/conclude that it's MORE LIKELY that Goddidit to create the complexity that we see, rather than that a handful of forces acting on atoms and matter (physics) and life (biochemistry) over billions of years according to rules we've been able to identify by carefully studying the universe? I would conclude THAT is much more likely than Goddidit. Evolution--change over time--occurred both with the atoms of the universe, becoming stars and planets, and with life, and resulted in millions of different species filling all the ecological niches on Earth. It is not only technically possible, all the evidence shows that it is indeed what has happened--the unfounded arguments of creationists notwithstanding. And yes, it is highly unlikely that we humans are here...there was nothing inevitable about humans coming into existence through entirely random processes...but here we are!
You can choose to bet on God doing it, but the evidence points to natural processes.
One can argue, of course, that God uses the laws of nature and evolution to create us, but that seems to be adding an unnecessary component to the explanation of the universe...an explanation that at the same time seems to rob humans of their ability to choose.