Infinitely small and infinitely large are imo impractical concepts. An infinitely large universe could not expand because (by definition) it's already as big as it can possibly be. It can't be or get any larger than infinitely large, so expansion would be out of the question.
I think my neighbor was approaching the idea of finite matter in an infinite universe from a diff ...[text shortened]... nfinitely large bucket. From my pov there is no bucket, and that finite blob of mud is all there is.
A universe is a cylinder one parsec in radius and infinitely long. This is an "infinitely large" universe insofar as it has infinite volume.
Now...start increasing the radius...2 parsecs...3...4...and so on... The "infinitely large" universe is expanding.
Your definition of "infinitely large" is hinted at but not explicated. If it's "Anything so large that it cannot get larger," you're just saying that an infinitely large universe occupies every point in some "space" that, I must presume, has been arbitrarily chosen to be three-dimensional. But just as a plane (an "infinitely large area") can be expanded into three-dimensional space, the latter can be expanded into a fourth spatial dimension.
And we haven't even gotten to the issue of mass. How concerned are you with physics? Do we play by Queensbury rules and assume a quantized universe, or thumb our noses at luminaries from Heisenberg back to Democritus and assume that matter is infinitely divisible?
Forgetting quantization, gravity, and other physical considerations, we could conceive of a ball of matter with density equal to 1 at a point P in space, and let the density drop off according to an inverse-square rule: at a distance r from P the density will be 1/r^2. It's a simple calculus problem to show that such a ball of matter has finite total mass, despite its radius being infinite. So in this way we can see that a finite amount of mass could, subject to our (lack of) physical constraints, occupy an infinite volume of space.