Do I need a checkride for an initial SIC A320 type rating?
A PIC type supercedes and SIC type.  An SIC type is really just a formalism of 121 initial first officer training to satisfy specific ICAO requirements.  A typical route to an SIC type is airline ground school, FFS and then company checkride (no APD, no DE, just a check airman) and the issuance of the SIC type.  If you already had a PIC type you'd go through the same training and company check (required by company approved training), but you wouldn't get an SIC type as you already have a PIC type.

The FAA shouldn't require anything out of you if you are PIC typed already.  The company may require you to do the full FO training and the FO company checkride as part of its own FAA approved requirements.  If you want a more specific answer, you could provide more details about how your training is being conducted or you could ask your facilities training department or director of training.