I have had the same issue since launch. I have reset me router multiple times (including factory resets), uninstalled the game and reinstalled (to both internal and external storage devices), and gone thru various steps provided by EA support for port forwarding and such (UoTrace results had no issues). I'm still not able to connect to ME:A multiplayer. All I get is Network Error please try again later. I've tried various times of the day and not able to connect.
I have friends who are able to connect just fine to the game. The only difference I've seen between them and myself is they have the standard edition while I got the Deluxe, and they have different ISP's. I've checked with my ISP and they don't see any issues from their end. The odd thing is that my other EA games on both Xbox One (Battlefront, PvsZ, etc.) & Xbox 360 (like ME3) connect just fine to multiplayer. I even used my wife's profile to try and connect and can't get hers to work either - same error.
This is very frustrating as want to experience the multiplayer plus get my pre-order and Deluxe edition perks for my character to use in single player as well. For those having issues do you have the standard edition or a different version? Normally there wouldn't be a coding issue but who knows.