The growing volume of litigation in the Brazilian judiciary imposes significant challenges to procedural speed and efficiency. One critical bottleneck lies in the initial classification of petitions, where the correct assignment of the procedural "Class", as defined by the Unified Procedural Tables (TPU) of the National Council of Justice (CNJ), is essential for the subsequent procedural flow. Errors at this stage lead to rework and delays. This article investigates the potential of Artificial Intelligence to mitigate this issue by presenting a comparative analysis of the performance of two distinct technological approaches: the Automated Machine Learning (AutoML) framework AutoGluon and a suite of Large Language Models (LLMs) from Google’s Gemini and Gemma families. Using a private and robust dataset of 27,000 initial petitions from the Court of Justice of the State of Amazonas (TJ-AM), distributed across nine procedural classes, the models were evaluated in a zero-shot scenario simulating implementation with minimal configuration effort. The results for both technologies demonstrate remarkable feasibility. AutoGluon, leveraging the full dataset, achieved a performance ceiling of 95% accuracy. Impressively, the LLMs, evaluated on a smaller sample without specific training, delivered highly competitive results, with Gemini-2.0-flash reaching 94% and Gemma-3-27b-it achieving 93% accuracy. The study concludes that "out-of-the-box" AI solutions are promising tools for assisting lawyers and judicial staff, with the potential to improve classification accuracy, streamline workflows, and contribute to greater efficiency in the delivery of justice.