In 2010, you came across a site that was giving away bitcoins. The site said it was free money so you signed up. You were logging in to figure out how it was money but couldn't. The last time you logged in you had more than 100 bitcoins. Later you forgot about the site until 2017 when a ponzi was advertising Bitcoin. Bitcoin? The name rang a bell and you stated hearing stories. You remembered you must have many bitcoins somewhere but you can't even remember the name of the site. How would you recover your BTC?
You don't even remember the site, so why then do you talk about recovering it? There is no way you can recover your bitcoin if you don't know the site where it is stored and even if you do know the site, you will need your username and password to access your account on that site. So you should just forget about it and look for something else to do and earn bitcoin because as for going to get those coins, it's not going to work out.
The best thing you can do us to remember the site, and if possible that you still have your history from then on your browser you can scroll it up to that year and start checking for the site. But, I know for sure that most sites we had then no longer function now. I know one good faucet that used to be around back then and paying a high number of Sats, around 2017 when there was a bull run they stopped functioning and closed the site.