The contemporary urban environment faces such challenges as overloaded traffic, heavy pollution, and social problems, etc. The concept of the “smart city” allows solving some of these issues. One of the opportunities provided by the smart city is the development of micro-mobility and sharing services; contributing to the optimization of transport flows and decreasing carbon footprints. This study investigates the factors affecting the development of e-scooter sharing services and the attitudes of young urban residents towards using these services. The research applied a PLS-SEM (partial least squares structural equation modeling) analysis performed in SmartPLS3.7 software. The data were collected via focus groups and surveying a population aged 18–35. The authors partially based the research on the UTAUT model (the unified theory of acceptance and use of technology), taking such constructs as “intention to use”, “anxiety”, “attitude toward use”, “effort expectancy”, and “social influence”; they also introduced the new unique variables “internal uncertainty”, “e-scooter design”, “experience”, “perceived safety”, “infrastructure quality”, and “motivation to physical activity”. The main finding of the study was determining that the latent variables attitude towards sharing, anxiety, internal uncertainty, JTBD (jobs to be done), and new way of thinking have a direct or indirect effect on the intention to ride e-scooters in the future and/or to use sharing services. The obtained results permit making recommendations to businesses, municipal authorities, and other stakeholders on developing e-scooter sharing services as a contribution to the advancement of the smart city.