We cannot count them because our brains have limited cells and there are infinite galaxies.
No infinities.
Never.
When scientists speak of
The Universe, they almost always are speaking of the
Visible Universe. Which is some 13.8 billion years old (chronologically), and some 50-ish billion light years across (by proper time -- the width, at "present time", can be greater than the light-time age of the universe, because the fabric of the universe itself has expanded -- at the edges which are visible, it has since expanded away, faster than the speed of light. That's why stuff on the edge appears so extraordinarily old and distant.) Objects are not allowed to go faster, but the stretching of space itself can go at any speed it may. Remember, the Alcubierre drive is theoretically consistent, too.)
The whole Universe, including that outside the
visible, is (as far as we can tell) infinite. Or, there's no reason (as yet) to believe that it has any obvious extents, so it's as good as infinite.
It's very, very likely that there exists a uniform distribution of galaxies, outside of our visible horizon (beyond the visible universe). We just can't see it, except through tenuously inferred relationships (i.e., how the oldest galaxies, and CMB, have apparently been tugged around by consequent assumed mass distributions).
Tim