Dude, you absolutely should be trying to be a manager in 3 years, if you want to go down the management track.

Depending on company size, you should probably be a team-lead or something by then.

Junior developers that remain "solo" workers after 3+ years in the industry is a bad sign for value. If you've been developing for a while, at the very least you should be put in a leadership position from a project perspective. Management/leadership experience doesn't just pop up out of nowhere. It's a skill you have to work really, really hard at. Take every leadership opportunity you can grab. You don't have to be "the boss" in the formal sense of the word, but you absolutely should be working towards a leadership role.