IMO
The concept of inifinty and randomness are built on the same principle, that time actually matters. Like it or not, we invented the concept of time. We invented the second, the minute, the hour, the day, the week, month and year. None of that shyt actually matter outside of earth. Consider this, there's space mutants already doing there thing and our seconds are their hours. They move at hyper speeds because their mass is inheritently different...
Point im trying to get at is that we expect all our earth concepts to be univseral when they arent. Sure we have an idea of some of the laws such as a possible speed limit to light and overall gravitational attraction, but to think of all the billion of trillions of billions of planets are following our same rulles?
Back to the topic tho, infinity needs a divisor.. a common measurent. You cant just say something is inifinite distance, what if inifinite distance is the measure itself? What the fukk is a mile anyways? Random dives into probability, things dont get more random they just get less probable. Anything can and will happen if you give it enough... TIME! Which is our own measurement. So take away the human concept and you have anything can and will happen. Theres nothing random about that.
These concepts are only relavent from the human perspective. If anything, we need to consider the closest thing to randomness in this universe, which is the intangible consciousness. We are able to concieve thoughts that we cant explain such as infinite and random and time. We made these terms up after analyzing the world around us with our limited sensors (sight, sound, feel, etc). Just as dude posted earlier, it took us long enough to figure out properties of things we couldnt sense, why limit our understanding based on a already proven flawed system of sensing reality.
As for what i believe? Well people believed the world existed on a two dimensional plane for the longest just to find out it was a sphere. We think this univese is some sort of infinite 3 dimensional space, who's to say it doesnt extened into a higher dimension? Certainly we'll never know in our short lifespans.