Just observe what nature is doing. As soon as the grass starts into growth and weeds and flowers are growing is the time to do it. Also, you need to avoid doing anything in wet weather when the ground is saturated and the lawn likely to get compressed.
Feeding is probably the most important thing to do, and moss tends to disappear anyway in warm, dryer weather. Unless you have a huge lawn, I would have thought forking it would be more effective as you can go deeper, and then brush the sand to create deeper drainage through the holes made by the fork.
I would say late April to mid-May is the earliest to do this to best effect.