Cataclysmic variables (CV) encompass a diverse array of accreting white dwarf binary systems. Each class of CV represents a snapshot along an evolutionary journey, one with the potential to trigger a type Ia supernova event. The study of CVs offers valuable insights into binary evolution and accretion physics, with the rarest examples potentially providing the deepest insights. However, the escalating number of detected transients, coupled with our limited capacity to investigate them all, poses challenges in identifying such rarities. Machine learning (ML) plays a pivotal role in addressing this issue by facilitating the categorization of each detected transient into its respective transient class. Leveraging these techniques, we have developed a two-stage pipeline tailored to the Zwicky Transient Facility transient alert stream. The first stage is alerts filter aimed at removing non-CVs, while the latter is an ML classifier produced using Extreme Gradient Boosting, achieving a macro average area under the curve score of 0.92 for distinguishing between CV classes. By utilizing the generative topographic mapping algorithm with classifier posterior probabilities as input, we obtain representations indicating that CV evolutionary factors play a role in classifier performance, while the associated feature maps present a potent tool for identifying the features deemed most relevant for distinguishing between classes. Implementation of the pipeline in 2023 June yielded 51 intriguing candidates that are yet to be reported as CVs or classified with further granularity. Our classifier represents a significant step in the discovery and classification of different CV classes, a domain of research still in its infancy.