Satellite laser ranging (SLR) systems require precise time tagging in the order of a few picoseconds to accurately measure the time interval between the emission of a laser pulse and the detection of its response. Traditional SLR systems face challenges such as high noise levels, atmospheric interference, and limitations in time tagger design, resulting in the necessity to use complex gate generators that provide measurement within a very short time window. This study introduces a breakthrough in time tagger technology, enabling continuous event detection. Beyond enhancing SLR capabilities, this innovation opens new prospects for other applications, such as lidar and integrated sensing and communications (ISAC) in space. The research outlines the opportunities presented by continuous event recording, addressing potential limitations and challenges. Additionally, it provides a comprehensive introduction to the concept and presents modeling and practical experiment results conducted at a functioning SLR station.