Update: EA says it's been fixed.
We've cleared up the connectivity issues with #AnthemGame. Sorry for the bumpy landing into Fort Tarsis earlier today. Thanks for sticking with us, Freelancers!February 15, 2019
Original story: EA has acknowledged that some players are having issues connecting to Anthem's servers, and says it's working on a fix as quickly as possible. The game went live for Origin Access Premier users about an hour ago—while I personally encountered one brief server error screen, since then I've logged in and out twice as a test without any issues. Likewise, none of my PC Gamer colleagues—who were already logged into the game—have had any trouble. So it's hard to tell how widespread these issues are.
Here's how EA's Help account acknowledged the issue:
Hello, Freelancers! We understand some of you are having issues connecting to #AnthemGame servers right now and we’re working to address it as fast as we can. Please hang with us and try again in a few minutes.February 15, 2019
We'll update this post when EA provides an update on the issue, and we'll be playing and writing about Anthem all weekend. Keep an eye on Anthem's server status here (opens in new tab). Maybe, by the end of Sunday, I'll understand what the Anthem of Creation actually is.