Well, I think there's a hole in the second Earth paradox. For example, we can have an infinite range of numbers without any two numbers being 100% identical. I think same can apply to cosmic structures, they can be infinite without any being 100% similar.

Also since it takes time for these cosmic structures to form, it would mean that for an infinite universe to exist, it must have existed an infinite length of time. A universe that began at a certain point in time, whose age is not infinite, cannot be infinite in size, since it takes time for it to form.