Young exoplanets and their corresponding host stars are fascinating laboratories for constraining the time-scale of planetary evolution and planet-star interactions. However, because young stars are typically much more active than the older population, in order to discover more young exoplanets, greater knowledge of the wide array of young star variability is needed. Here Kohonen self-organizing maps (SOMs) are used to explore young star variability present in the first year of observations from the Transiting Exoplanet Survey Satellite (TESS), with such knowledge valuable to perform targeted detrending of young stars in the future. This technique was found to be particularly effective at separating the signals of young eclipsing binaries and potential transiting objects from stellar variability, a list of which are provided in this paper. The effect of pre-training the SOMs on known variability classes was tested, but found to be challenging without a significant training set from TESS. SOMs were also found to provide an intuitive and informative overview of leftover systematics in the TESS data, providing an important new way to characterize troublesome systematics in photometric data sets. This paper represents the first stage of the wider YOUNGSTER program, which will use a machine-learning- based approach to classification and targeted detrending of young stars in order to improve the recovery of smaller young exoplanets.