First of all, I suggest you let them go out and play. Let them learn how to use their bodies and move. Don't just immediately strap them into hockey skates or soccer cleats or something and have a singular focus.
There's not a lot of research on this, but the research that's out there suggests that kids who engage in a variety of activities at a level that's enjoyable for them develop better body awareness and have stronger capabilities to deal with bumps and falls and things like that, which can help minimize and potentially prevent injuries. That broader experience is huge.
So as parents, just let them get out, enjoy life, and play. But also help them understand that there's a right way and a wrong way to do things, so that they are equipped with the skills they need to engage in these activities.
Parents can take a role with that but also can ensure that coaches have the opportunity to understand how to take that approach as well.
I think almost all of us to a person have said that awareness of all the potential factors associated with injury needs to be first and foremost in our minds. Raising awareness is another piece I would recommend.