So let's review facts as we observe them without conclussions first.
1. The atom and every chemical compound in a rock or in us is governed by the electrical force.
2. Without electrical forces you could not move, breathe and your heart would not beat and no blood would flow.
3. Electrical forces are everywhere we have ever gone and took readings. Not a single space probe has reported negative results, ever.
4. Without electrical forces in your brain we couldn't have this discussion.
So, calculate the odds that electrical forces in the universe won't form a conscious mind.
Sometimes paradoxes arise science is unable to answer, it's the way things work.
Boltzmann brain - Wikipedia, the free encyclopedia
[hep-th/0208013] Disturbing Implications of a Cosmological Constant
I would say the odds of a being of electrical thought is much higher than one having to form from non-living matter to begin with, and then slowly evolve over billions of years into something finally able to become conscious. The odds are better for the intelligences to exist in the universe than they are for you to exist. Yet I do not see you objecting to the odds life formed from non-life. Therefore you accept these odds as not only highly possible, but as factual.
We would not be here discussing this if it was not for electrical interactions. I mean you still claim to be measuring electrical interactions from the initial Big Bang. Unless you think the CMB is not an Electromagnetic event? You want expansion to be caused by some form of energy. Everything we see is emitting an excess of electromagnetic radiation constantly as well.
I would say the odds are stacked highly in favor of a mind or minds existing in the universe. Can I prove it? No, but neither can one disprove it. You and I can't prove life evolved from non-life either, but what is the alternative? So you gotta have faith any way you go. My faith just has a better chance of being true than yours is all.
The odds against us forming is astronomical, yet science routinely considers the possibility of it occurring everywhere throughout the universe as a given fact, hence their probes to Mars to detect life, possibly Titan, and other planets orbiting other suns. Don't see you objecting to the odds once again.