The rapid advancement of artificial intelligence and its increasing societal impacts have turned many computing educators' focus toward early education in machine learning (ML). Limited options for educational tools for teaching novice learners about the mechanisms of ML and data-driven systems presents a recognized challenge in K-12 computing education. In response, we introduce "GenAI Teachable Machine," a visual, data-driven design platform aimed at introducing novice learners to fundamental ML concepts and workflows, particularly in the context of classifiers. Following the design science research (DSR) method, this study presents the prior recommendations, standards, codevelopment, and extensive field testing that resulted in a platform enabling young learners to express their own interest-driven ideas through codesigning and sharing personally meaningful apps. The platform improves on the design of Google's popular Teachable Machine 2 by its ability to create a standalone app by defining one or more actions to be triggered by each classifier result, and deploy that app to other devices. It also enables one to distribute the collection of training data among many users. In addition to the DSR process, this article presents findings from usability lab tests (N = 8) and 6-h classroom projects involving fourth and seventh grade children (N = 213). The results show that children who had no experience of ML were able to navigate through the workflow and turn their own ideas into concrete ML-based apps. The majority of children were able to reflect and present, in their own words, their working process using data-driven (design) thinking concepts and insights.