When a person becomes an entrepreneur? I am not sure but I would guess it is from the very first moment. The moment of the initial idea. When you are sleeping on your bad and you can't sleep because you are having a brainstorming. You just take a notebook and try to writedown as fast as possible all those ideas.
And on the day after in the morning, you call someone and tell this person that you shall do it. It comes from inside. It is our internal voice talking to us.
It was the way I have started and I would guess the beginning of other entrepreneurs. Just never give up.
Then, you start to work and you spend money and time to realize that this was the wrong way. Then you fail and you try again and you fail again. And people around you begin to ask you and doubt and they do not believe you. You feel alone. Few people believe. And time and money and the conditions are harder.
Challenges are your routine, rediscover yourself or maybe simply reinvent and question your own values. Those are the characteristics of an entrepreneur. Only by overcoming challenges you will be able to succeed.