Hello. As I said, yes I am American, and yes a judge would hand down a sentence to a defendant who'd been determined by the jury to be guilty. And yes, the way a common law works is precedent is established by trial as situations arise.

You make an interesting point that a judge can't possibly serve everyone's ideal version of justice. This is true. In fact, no system will ever be able to serve everyone's ideal form of justice. It simply isn't possible unless we all agree, and history has shown us that this has yet to occur. What a judge will be able to do, is to hand down that sentence. Which is why choosing the right judge is important, and why they're publicly elected. In casting that vote, what the voter says is "you have my confidence to make a fair decision." Not necessarily an ideal decision, but a decision that can be the basis -the precedent you seek- for future instances.

If your argument is that civil law would be a better fit in this situation, that's fine. We can talk about that. But saying there's no basis of law in a place where we're trying to establish the law is redundant. Whatever we'd like to found this new society on, we're deciding that here and now, just as the founders of the new American society did when they decided to throw away the established precedent of Colonial rule.