Context. A defining characteristic of active galactic nuclei (AGN) that distinguishes them from other astronomical sources is their stochastic variability, which is observable across the entire electromagnetic spectrum. Upcoming optical wide-field surveys, such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time, are set to transform astronomy by delivering unprecedented volumes of data for time domain studies. This data influx will require the development of the expertise and methodologies necessary to manage and analyze it effectively. Aims. This project focuses on optimizing AGN selection through optical variability in wide-field surveys and aims to reduce the bias against obscured AGN. We tested a random forest (RF) algorithm trained on various feature sets to select AGN. The initial dataset consisted of 54 observations in the r-band and 25 in the g-band of the COSMOS field, captured with the VLT Survey Telescope over a 3.3-year baseline. Methods. Our analysis relies on feature sets derived separately from either band plus a set of features combining data from both bands, mostly characterizing AGN on the basis of their variability properties and obtained from their light curves. We trained multiple RF classifiers using different subsets of selected features and assessed their performance via targeted metrics. Results. Our tests provide valuable insights into the use of multiband and multivisit data for AGN identification. We compared our findings with previous studies and dedicated part of the analysis to potential enhancements in selecting obscured AGN. The expertise gained and the methodologies developed here are readily applicable to datasets from other ground- and space-based missions.