I think you are thinking in terms of area. That's not what I'm talking about. Let me put it this way: Do you think the universe has been around for an infinite amount of time and will be around for an infinite amount of time? Do you think the universe contains an infinite amount of matter and energy? If not, then the universe is not "infinite" in the ways that matter most. It's not the space that creates solar systems or life but the matter and energy that occupies it, concentrating and combining over time. I'm not aware of anyone who is claiming that the universe contains an infinite amount of matter and/or energy and the jury seems to be out on whether the universe will end or not.