This research investigates how entrepreneurs of small and medium enterprises (SMEs) with inadequate capabilities and limited resources drove digital transformation in their companies, a phenomenon that remains under‐researched in the extant literature. We conduct qualitative research on digital transformation to cross‐border e‐commerce undergone by 7 SMEs on the Alibaba digital platform. We inductively derive a process model that aims to describe and explain how SME entrepreneurs, with support from the digital platform service provider, drive digital transformation through managerial cognition renewal, managerial social capital development, business team building, and organizational capability building. This model expands our understanding of both digital entrepreneurship and digital transformation. It also presents new insights into how digital platform service providers can help SMEs transform and compete.