I want to start by defining infinite as applied to our universe, that is infinite in size in all dimensions, no beginning no end just always existing.
In practice, of course, the universe is far from steady and very much dynamic. Our solar system is an example of this our planets and sun are made up of elements which have been made up in nova and super nova star explosions which exported their materials through out our galaxy. Our solar system as it moves through interstellar space accumulates these elements and is steadily growing in mass.
What is the life time of a nova or supernova star? a billion, 5 billion or 10 billion years. There just is not enough time in the big bang model ( a life time for the universe of 12 to 16 billion years they suggest?) to spread the elements to build star systems.
In the infinite universe our galaxy is constantly being seeded by nova explosions, so interstellar space will be a vast dust ( up to dead star size) cloud. Star systems trawl through this attracting material into their respective solar systems. Our solar systems Oort cloud is evidence of material being swept up by the sun.
A supernova at the edge of a galaxy will blow material free of that galaxy into intergalactic space and I believe the galaxy has its own equivalent of an Oort cloud at its margins. So there is dust and bigger in intergalactic space.
Space is not an "empty pristine void" rather there is "dust" out there. (Is this the dark matter they are looking for?)
I have never been happy with the red shift theory of the universes expansion.
Astronomers work at night and they must see some magnificent sun sets and sunrises. Those glorious ones where the dust in the atmosphere gives lovely red skies.
So why have they discounted the tired light explanation for red shift? At a given observational radius from earth the blue shift of galaxies stops. It stops because the light is overwhelmed by the effect of tired light. From that point out as light battles its way through more and more galactic "dust" the red shift becomes greater due to distance travelled, nothing to do with advancing or retreating from us.
To summarize there is not enough time in the big bang theory to accumulate the material to form even our own solar system.
There is an explanation for the red shift that does not mean the universe is expanding.