Seeing old posts from other instances that were published before you followed

Recently, I've set up my own Mastodon server and immediately run into the infamous issue of not being able to see my posts from other instances. As it turned out, posts from other servers are cached to be displayed, but caching only happens after somebody starts to follow the profile in question. Because my instance is small, this basically means nobody will see my posts, which ruins the whole point of running my own server.

Is this a Mastodon only issue or is it just the way Fediverse works? Are there any alternatives to Mastodon that allow seeing the entire timeline without following? Does Lemmy share the same issue?