well, i dont think you should worry about waiting for a period unless
you have something specific in mind.
It depends on what you mean when you say the soil is 'stagnant' and
needs some air. The idea of 'dead' soil is quite a real one but it
means things like - there is little hummus in the soil or that there is
little in terms of beneficial microbes which help plants grow.
Which i dont think is particularly crucial for growing grass.
You may find that a good dig does the ground a world of good.