New players

[jz2016cubs_PSN]

So I’m currently in double a with the cubs. Have had this player for a week or two. Seiya Suzuki just got added to the game. Is there a way to get him onto the big league squad to play with him when I make it to the majors? Or would I have to start over?

[Yardem Hane_XBL]

Suzuki will be added to the Cubs roster at some point through a patch. However, he will probably not appear in your career, you would have to start over after the patch. When you start a new career, you choose "current rosters", and the teams will have the rosters that are active at that time.
The good news is that your ballplayer progress will continue from where you are, so I'd suggest keep upgrading your player until Suzuki appears, and then decide whether to start a new career file.