c'est la vie
as others have said, it's just the way things are in life and that translates into all social interactions. I feel for you on the established FCs. I joined my FC in the early days of ARR launch. However, the FC had migrated from an older server and had been playing together since 1.0's days. It took awhile (and lots of FC chats and runs), but I have felt at home in the FC for some time. But I certainly felt like a bit of an outsider for the first month or so. My FC is currently at 126 people and there are definitely times I am running around the server and spot someone in my FC and I have no idea who that person is.

My suggestions to you would be:
a) start a FC or join a smaller one
b) be talkative in FC chat, so that your name at least becomes recognizable
c) offer to help other FC players (crafting, warm body in dungeons, etc.)
d) roll a tank (insta-friends! your mileage may vary)

There are a lot of newer people in my FC as a result of recent recruitment. However, I'm starting to recognize names and personalities just because they are talking in the chat and offering/asking for help. Just be proactive and hang in there (esp for a larger FC). Don't take others' silence as being dismissive.