It's currently the rage in blackhat SEO: just say you're John Doe from Doeville and competitorsite.com is infringing on your copyright. Google will remove that specific URL from the SERPs and there's a 50/50 chance whether the target gets a notification from google or not.
If they do, they can counter claim directly and it takes 12-48 hours to be reinstated.
If they don't, they have to figure out what's going on by using the Lumen Database (the only way to receive that information because Google is horribly bad at basic legal matters) and finding the notice, which will contain the exact URL (because fun fact: the claim and counter-claim are case-sensitive, the removal-from-serp is case-insensitive), and then do manual counter-claim, and it takes anywhere from 3 to 30 days.
During that time, your competitor will just be gone from the SERPs.