The security of real-world quantum key distribution (QKD) critically depends on the number of data points the system can collect in a finite time interval. To date, state-of-the-art finite-key security analyses require block lengths in the order of to obtain positive secret keys. This requirement, however, can be very difficult to achieve in practice, especially in the case of entanglement-based satellite QKD, where the overall channel loss can go up to 70 dB or more. Here, we provide an improved finite-key security analysis which reduces the block length requirement by 14% to 17% for standard channel and protocol settings. In practical terms, this reduction could save entanglement-based satellite QKD weeks of measurement time and resources, thereby bringing space-based QKD technology closer to reality. As an application, we use the improved analysis to show that the recently reported Micius QKD satellite is capable of generating positive secret keys with a security level.