Infinite would mean in simple terms; the thing that has no known bound.

The number of sand particles on earth is finite as it is restrained to a specific geographic area where each particle is known to occupy a certain volume. We can therefore easily bound the number of these particles thus that number is finite and countable.

When it comes to the question of whether the Galaxy is finite or infinite, I can safely say that it is possible to estimate the number of particles within the defined bounds of a certain galaxy which leads us to conclude that a Galaxy is also within the realm of the finite.