What is the story behind the age of 40? Is it the age of Nabuwat?

In my childhood, We were told in books that when the prophet reached the age of 40, **that is the age when prophethood is revealed**, the Angel Gabriel appeared to him in the Cave of Hira. **My question is, is there any evidence that 40 is the age of Risalaut?** As an argument, I can say that Jesus did not wait till 40 to become prophet. Also Moses AFAIK did not receive revelation at 40. What is the story behind the ago of 40 as the age of Nabuwat or Risalut. I can further argue that if the prophet was declared at an early age, he would have more time preaching the religion and thus fulfilling Allah duties better since the person will be in better health and will have more time preaching the religion.