can I restore my SMS messages without iCloud? I sold my iPhone 7, I don't have iCloud backups nor set it to save messages to iCloud.  I wonder if I can have them restored to a new iPhone or Android phone, are they saved by the carrier?  (carrier is Three). All I have is the my SIM card.
Any help much welcome.
No, if you don't have any backups in iCloud or your local Mac or PC, you can't restore them.  You don't have any place to restore them from.
The SIM card does not store a copy of messages sent using iMessage or Messages.