Not quite sure what you mean by "start its thing". That could be taken a few different ways.
Each chicken, male and female, has it own personality. They don't all act the same. They mature at different rates. The interactions of chicken society can be pretty complex. Each flock has its own dynamics based on those personalities and flock make-up. Finnie mentioned that a dominant rooster can intimidate a less dominant cockerel. A strongly dominant hen can have the same effect on a weaker cockerel.
If you mean when will he start mating the girls, he may already be and you haven't noticed. It's not always a wild cockerel pillaging and raping as he lays waste to the area. Or the hens may have him so intimidated he doesn't even try. What I often see is that some hens accept his advances and willingly squat while others don't. They may run from him or they may fight him. The dominant hen can knock him off if he tries to mate a willing hen. Some cockerels start trying to mate and dominate other chickens, even mature hens, as young as 12 weeks. Others can wait close to a year. So what is a sign that he is starting to mate the girls? When you see him, if he isn't already.
When will he start taking care of his flock? Finding them food and calling them over, warning the flock of danger, breaking up fights and keep peace in his flock? Maybe helping the hens find a good nest or rounding them up at night? A lot don't do all of this. But that happens when he matures to the point that it is his flock or he wants it to be. The personality of your dominant hen can have a big effect on this if she is strong. To me the best combination is a dominant hen that is still dominant but isn't that strong while the boy has a strong personality, he can often win them all over pretty peacefully. But a weak cockerel and a strong battle axe of a dominant hen that doesn't give any quarter can get violent. With most of mine that take-over happens when he is around 7 months old and is usually pretty peaceful. But I have had a cockerel take over as young as 5 months (that was peaceful), and one that waited 11 months (that was not peaceful).
I don't know of any physical signs or any appearance changes in a cockerel that signals any of this. This is all behavioral. The only signs I know of that show he is going to start doing any of these things is when he does. It may be a smooth transition, it may be violent. You never know.
