With the idea that “Our sense of justice is imparted to us by our Creator God” I don’t think it means that the judge or whoever has to believe in god themselves. They’re a vehicle through which god works, whether they are aware or oblivious to it themselves.
But I don't believe God exists. And who is to say I am wrong? I love the take that Douglas Adams has on this - using the Babel Fish as an example. If you aren't familiar with the Hitchhiker's Guide to the Galaxy, the Babel Fish is a small fish that you put in your ear and it acts as a universal translator (and hence where the current website of the same name got its title!):
Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as the final and clinching proof of the non-existence of God. The argument goes something like this: "I refuse to prove that I exist,'" says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
Someone who believes in God believes that my sense of justice is imparted from God regardless of my lack of belief. I believe that my sense of justice comes from the family, community and society in which I was raised. If you cannot prove God's existence, then how can you prove justice? And how can you defend the concept of divine justice when people murder and maim others who are innocent, in the name of God?
We have all inherited our sense of justice from centuries of faith based ideas such as the 10 commandments. It’s hard to say we act without influence from those faith ideas because we don’t.
You can equally say that we are influenced by community folklore. I'm sure you're aware that Christmas as a religious festival was co-opted by the church to discourage paganism. Faith is not the only driver of justice - and justice is not a consistent and universal concept. An evangelical Christian may feel justified in refusing service to someone who is gay. They would argue that they are just in their decision - I would argue that they are not. You are trying to treat 'justice' as if it is a single, fixed and universal point, but that's not the reality. Islamic terrorists feel they are justified in killing non-believers in the name of their cause. Christian far-right terrorists feel they are justified in murdering doctors and blowing up health facilities where abortions are performed. Neither of those circumstances meet my idea of what justice is.