> Universe is infinite. It means, that we can zoom up infinitely AND we can zoom down infinitely, which means that space always filled with something, and this something have a temperature.

I'm not sure this follows. The set of positive integers is infinite. It means that there's always a larger integer, but it doesn't mean there's always a smaller one, or an infinite number of integers between 1 and 10.

Even in this case, there is infinitely small chance that we are sitting so close to the beginning of everything.

This is only true if we pick a scale with a fair infinite-sided dice.

If it is as we suppose that the universe started all squeezed into a point at the beginning of time, and then explosively expanding out from there, then I don't see why we would expect a uniform distribution like that.

Replace integers with rationals or reals.

Having four legs doesn't follow from something being an animal just because there are examples of animals with four legs. A chicken is also an animal.

Having four legs is accidental to being an animal, just as there being an infinite number of elements between any two elements in a set is accidental to its cardinality being infinite.

Chickens have wings at the end of their arms.

We don't have any conclusive evidence about the universe's finitude nor its discreteness.

The universe is not infinite.

Nothing is infinite

It isn't infinite even if the universe is expanding forever - which is not commonly accepted as the big crunch exists as an idea.

Just bc we may never be able to see the whole picture doesn't mean there isn't one.

why isn't it? What prevents that?

> AND we can zoom down infinitely,

Wouldn't you run into the planck length at some point?