People have questioned if it was possible to have a future American government without a judicial branch and the answer is yes, it is possible to have a functioning government without any judges and the answer lies in Ancient Rome.

Tribune of the plebs, tribune of the people or plebeian tribune (Latin: tribunus plebis) was the first office of the Roman state that was open to the plebeians, and was, throughout the history of the Republic, the most important check on the power of the Roman Senate and magistrates. These tribunes had the power to convene and preside over the Concilium Plebis (people's assembly); to summon the senate; to propose legislation; and to intervene on behalf of plebeians in legal matters; but the most significant power was to veto the actions of the consuls and other magistrates, thus protecting the interests of the plebeians as a class. The tribunes of the plebs were typically found seated on special benches set up for them in the Roman Forum. The tribunes were sacrosanct, meaning that any assault on their person was punishable by death.

https://en.wikipedia.org/wiki/Tribune_of_the_plebs