What should my greetings be when I'm sending an e-mail to a staff whose gender I don't know?

Dear friends and associates,
Dear Sir/Madam,
Ladies and gentlemen,
and in a very formal way, though not often used – mesdames et messieurs.

find out their gender.

If your staff comprises more than one person, how about “Dear staff”, Greetings, All” or “To All”?

I usually will open with “Greetings Gentlemen” when I know the gender, obviously in that case it’s men. If they’re women who I’m friendly with, I’ll write “Hi Ladies.” In the example you give where you don’t know the gender, I would just start writing, or if I wanted to be a bit more structured, I’d write “hello” as an opener.

If it is an informal situation (not a job inquiry) I use Hello [company or department].

For example, when writing email for customer service, I would write “Hell Fluther” or “Hello Service Department”.

Similar to what @jaytkay recommends, I often use : “Dear <company> Staff, ...”
Also, email is quite a bit less formal than other media so you have a lot of leeway.

As in one person or a group of people? If it’s just one person is say, “Good morning/afternoon.” I work for attorneys, so a professional environment, but even there no one is so formal in an email to use, “Dear Sir/Madam.”

To avoid being labeled as sexist, you should never consider their gender. “To whom it may concern:” “Salutations, one and all!”

Or just assume that they are all women and always go with “ladies”.

Or avoid the uncertainty by opening with “Greetings—”.

‘Puny humans’

@Pachy got in before me with “Greetings all”.

Greetings! I hate when I don’t read the other responses before answering and then do that.

Thanks for all the useful ideas!^^