"It is a familiar moment."
Μετάφραση:Είναι μία οικεία στιγμή.
I don't think so (unless it has a meaning in Greek that I haven't come across yet). Familiar/οικείος means something that you recognise from prior contact. οικογενειακός/familial means something to do with a family. I'm not fluent yet though so I'm happy to be corrected.