My daughter claimed my partner's (now husband of 10+ years) nieces as her cousins almost immediately. She was 3 and absolutely loved her slightly older cousins. She was much slower to decide that the rest of his family were 'hers', although she always liked them all.
I think it is up to each family TBH. Interestingly my son (with my husband) recently wrote about his family at school and listed his "Mum, Dad, annoying step-sister and 2 baby cousins" without any mention of his older cousins, so clearly kids have their own ideas of which family members are important.
(I did say that 'annoying' was a bit rude and she was actually his half-sister if we were being accurate, I've never heard him refer to her as anything other than his sister before, think he wanted to be different maybe.)