I agree that the ability to measure distance would be very good. It is in today's soldiers. Someone with experience should have a very good sense of ranges up to 5 km. Closer range estimation (under 300m) can be very precise. This is driven by knowledge of weapon capabilities, frontages that can be covered, required dispersion, length and number of bounds to an objective and so on. Much as Soult at Austerlitz knew he needed 20 minutes to reach the Pratzen heights, we know how long it takes to cover ground. Back then they had to be extremely aware of intervals when marching column, and the requirement remains the same on today's parade square.
Let's say that a unit had trained to fire at screen targets at 100m (or any other range). I can easily see that the CO would give the order to fire as the attacking unit hit that mark.
It is also worth considering that defending units may have marked their ground. Today we sometimes place inconspicuous markers at certain distances from some firing points. This can be very useful on featureless ground that may become obscured by smoke.