Do the bylaws state a deadline for the audits to be completed? If that deadline has not yet passed, that may be why they are not handing over the copies yet. Audits take time and just because it is a new year does not mean they have been completed yet.
Generally speaking, it would be the homeowners association that would be sued by the individual homeowner. The homeowner has the right under Georgia law to inspect the records of the HOA. If those records are not made available, then the homeowner can sue to enforce that right in state courts. The management company may be listed as a second defendant, but you definitely need the HOA on the suit because that is who you have the relationship with.
However, you may want to check your restrictive covenants as well as the Association's bylaws. You may have additional remedies there or you may have additional steps to take if there is some kind of breach. There may even be some sort of mediation or arbitration clause that you need to comply with.
As a practical matter, talk to someone on the board of directors. Usually the management company will respond better to them than to the individual homeowners. From my experience, both personally and professionally, they are not turning over the audited accounts because they have not been audited. It may be because the property management company is not doing its job or because the deadline has not yet passed.