Question about applying for a U.S. green card while living in Canada as a commuter couple

I’m a Canadian citizen. I registered my marriage to a U.S. citizen, and I plan to work in Canada and live as a commuter couple. I’d like to know if I need to apply for a U.S. green card right after marrying, or if I can live under my Canadian status without applying, or apply for the green card only when I eventually move to the U.S. years from now.