Very few sites allow the general public to view deleted (or "removed") posts. Typically, you need to have a subpoena (or another big stick) or be the original poster to get access to deleted content from the site itself. And both of those methods only work for as long as the deleted data is stored.
Reddit is the only site that I know of where "deleted" content is merely made slightly less convenient to view. Apparently, moderators can only remove a message from their subreddit. The content still exists on the poster's profile, and tools like Reveddit make it trivial for anyone to see. (It's all fun and games until you realize that despicable content is still up for viewing.) The original poster seems to be able to remove the content of their messages via editing, but if they delete the message without doing so it's still visible on their profile. Even with editing, I think there's still evidence they posted something where they did unless they delete their account — but I think this still may leave a message stub attributed to "[deleted]". (Not a Reddit expert, so correct me if I'm wrong.)
But that's the exception. I don't know of any other site that has even half of that (other than maybe Stack Exchange). For sites like Twitter, your most reliable sources may be external sites.
For notable people, there's someone out there recording everything they say, such as Politwoops for politicians (and political candidates). Many of these services are automated and are able to record even very short lived Tweets — there's one on Politwhoops that was "Deleted after 13 seconds". ETA: Politiwhoops is dead.
For anyone who's not being tracked like that, you may get very lucky and be able to find another site that captured the page. Archive.org is the biggest but not the only one. Google itself may also catch some posts, but only briefly, so try to archive the page if that's your evidence (example showing results for the now-defunct Lexico site — these pages have been dead for weeks now).
There are still more ways to provide evidence beyond that, but it's not always strong evidence:
- Responses to the deleted post, assuming that deletion doesn't remove the entire thread.
- Other screenshots (or quotes, or even just a confirmation that it happened) from independent sources. (The strength of this depends on who the independent source is.)
- Statements by the alleged original poster
- Saying something similar elsewhere.
- Comments that confirm or deny the alleged post. (This is fine to include with other stronger evidence or even by itself when the comment doesn't make them look good. But it's typically too weak on its own.)
- Evidence that someone else was the author. (Yes, two people can say the same thing. Yes, people have alts. In my experience, it's been strong evidence nonetheless.)
This isn't a comprehensive list. There might be other types of acceptable evidence out there. Or it might be impossible to provide evidence either way, like many non-science questions on Skeptics.
