For many couples, while their relationship is still fun and enjoyable after they pass the six-month mark, this is when it's time to think seriously about whether this is going somewhere.
There is no set time that you have to introduce your boyfriend to your friends and your parents and siblings (or not, of course, if you're an only child).
However, you would want to do that before you have been a couple for six months.
This is only going to lead to tension and fights, not the love story that you're expecting.
While some people like to act the same as they did when they were single, for the most part, when you're in a relationship, you spend a lot of time with that person.
You are compatible and both want the same thing: to feel connected to each other on a regular basis and hang out all of the time.