Hi
Here's how to transfer your swgoh game from one phone to another if you haven't logged in to Game Center.
You need iTunes first of all.
Then you have to open up on iTunes your device.
You then have to do an encrypted back up of your old phone. This will need a password of your making.
Then swap over to your new phone and do a restore.
Make sure after starting your phone to turn Game Center off and all should be good.
I've just spent 2 ridiculously frustrating days talking to EA to try and sort it.