I am an EP holder, and my age is 38, while my son is 11 years old. What is the cut-off date before I can file PR application to maximize my chances of success, considering it is my first attempt?

There is nothing like a cut-off date for a Singapore PR application. If you are an EP holder and have worked for a few years in Singapore, you are eligible to apply. However, your son will be liable for National Services if you sponsor his PR application. The national service liability arises at the age of completing 12. Meaning once your son attains this age (and if he is PR) then he is liable to serve national service at the age of 18.