Have a computer in a common space like the living room for when they want to be online. You don't have to be watching over their shoulder.
You could try to keep up with all the shit you have to be wary of your kids encountering online (e.g., age-inappropriate pornography, political extremism, social media "influencers", games with microtransactions, etc.) or you could be proactive and intentional and just nip it in the bud with how and when and where they have access to the online world at the access point.
There's a reason we wait until kids are 16 to give the freedom to drive a heavy hunk of metal at speeds that can kill themselves or other people. We should seriously re-evaluate when we give them the freedom to encounter the worst of humanity. The internet of the 90s and early 2000s is a distant memory; we live in a world of carefully engineered experiences designed to exploit our minds' flaws, online social environments our minds never evolved to navigate, and a host of other things I could mention that suggest that we should focus on providing childhoods in which they're engaged in things we know to be relatively safe, if not beneficial (e.g., play outside, read books, watch movies, play video games that aren't connected to the internet, etc.).