Time-domain astrophysics continues to grow rapidly, with the inception of new surveys drastically increasing data volumes. Democratized, distributed approaches to training sets for machine learning classifiers are crucial to make the most of this torrent of discovery - with citizen science approaches proving effective at meeting these requirements. In this paper, we describe the creation of and the initial results from the Kilonova Seekers citizen science project, built to find transient phenomena from the GOTO telescopes in near real-time. Kilonova Seekers launched in 2023 July and received over 600 000 classifications from approximately 2000 volunteers over the course of the LIGO-Virgo-KAGRA O4a observing run. During this time, the project has yielded 20 discoveries, generated a 'gold-standard' training set of 17 682 detections for augmenting deep-learned classifiers, and measured the performance and biases of Zooniverse volunteers on real-bogus classification. This project will continue throughout the lifetime of GOTO, pushing candidates at ever-greater cadence, and directly facilitate the next-generation classification algorithms currently in development.