Be the person at family dinner who asks the cousin nobody talks to how her week was.

Every gathering has an established pattern of who talks to whom, and somebody ends up outside it every time, not through any decision but through habit. Breaking the pattern costs one conversation and is noticed far more by the person included than by anyone else. It is a small act that reads as being seen, which is not a small thing to receive.

At the next family thing, sit next to the person who usually gets skipped and ask about something specific in their week. Ask a follow-up. That is the whole move, and it will probably be the part of the evening they remember.