On 1 April 2022, the AlfaCrux CubeSat was launched by the Falcon 9 Transporter-4 mission, the fourth SpaceX dedicated smallsat rideshare program mission, from Space Launch Complex 40 at Cape Canaveral Space Force Station in Florida into a Sun-synchronous orbit at 500 km. AlfaCrux is an amateur radio and educational mission to provide learning and scientific benefits in the context of small satellite missions. It is an opportunity for theoretical and practical learning about the technical management, systems design, communication, orbital mechanics, development, integration, and operation of small satellites. The AlfaCrux payload, a software-defined radio hardware, is responsible for two main services, which are a digital packet repeater and a store-and-forward system. In the ground segment, a cloud-computing-based command and control station has been developed, together with an open access online platform to access and visualize the main information of the AlfaCrux telemetry and user data and experiments. It also becomes an in-orbit database reference to be used for different studies concerned with, for instance, radio propagation, attitude reconstruction, data-driven calibration algorithms for satellite sensors, among others. In this context, this paper describes the AlfaCrux mission, its main subsystems, and the achievements obtained in the early orbit phase. Scientific and engineering assessments conducted with the spacecraft operations to tackle unexpected behaviors in the ground station and also to better understand the space environment are also presented and discussed.