"大家" means everybody/everyone. Maybe it is an idiomatic expression. "大家" literally means "big house".
In Spanish, we say "todo el mundo". It literally means "all the world".
I you'll find think it means "big family" even though there is no 人 after 家
家 can mean home or family. It's also a "classifier for families or businesses". Like in这 家 饭 馆 or This family restaurant.
Since Chinese are very family orientated people and the Han Chinese in particular see themselves as one family, I go with the family not house option.
It's also quite nice to think that everyone is the big family.
Politicians in Malaysia use this sentence to greet before giving speech.
It's funny that it won't accept the answer: Is everyone good?
Because that is literally what it says in Chinese.