There are also some fanfiction communities on Reddit. Subreddits dedicated to the show that Dean and Cas are from might have threads where fans share their favorite fanfics about the first kiss. You could also join relevant Facebook groups. But be aware that the search functionality on Facebook groups might not be as efficient as on dedicated fanfiction platforms.
Well, Fanfiction.net is another place to search. However, AO3 generally has a more diverse and inclusive collection. When you're on these sites, make sure to read the tags carefully. Some might be part of a larger series or have specific themes that you may or may not be interested in. For example, some might be set in an alternate universe where the characters have different occupations or backstories.
You can start by looking on popular fanfiction platforms like Archive of Our Own (AO3). There are tons of stories there. Just type in 'Dean and Cas first kiss' in the search bar, and you'll get a long list of relevant fanfics. You can also check out Tumblr. Some fans might post links or even write short ficlets about it there.