While the responses from both Zigner and FlyingRon are pertinent to your question, even if you weren’t time-barred for appeal, there is a more basic reason that you won’t accomplish anything through the court: most courts return all exhibits and other documentary evidence to the parties at the conclusion of the case (viz. the court has nothing for you to purchase, copy etc.). When there is an appeal to the superior court, the parties must bring their evidence and reintroduce it at that trial, and you noted that an appeal is not even an issue. There is no mandate to retain/store small claims evidence.
This practice relieves the court of the burden of storing the evidence (which would otherwise be the responsibility of the clerk) and reduces the volume of documents that would have to be transferred to the superior court in the event of appeal.
Even if, hypothetically, the court wished to review a complex document or there was some similar situation which prompted the bench officer to retain evidence, “take a case under submission” and not rule at the conclusion of the hearing, the common practice would either be to make a (disposable) copy and return the original to the party offering the evidence or, if that was not feasible, to tell the party to return to court to “pick it up [within a matter of days] or it will simply be destroyed”. People tend not to return and, even if you saw a document retained, it’s not there 30+ days later.