Applying for a job in Japan with COE (while living overseas)

Hello my company has offered me a transfer to the Japan office and will offer me a contract offer once my Spouse Visa is approved.
However currently I am living in Australia with my Japanese wife and expect to get the COE from the immigration lawyer (located in Tokyo) around May.

Apparently, once I get the COE from the immigration lawyer I’ll get the “green card” once I arrive at the airport in Japan, is that correct?

My question is can I sign the employment contract just with the COE before arriving in Japan and getting the green card at the airport?

Thanks for your help!