We present a pioneering estimate of the global yearly greenhouse gas emissions of a large-scale Astrophysics experiment over several decades: the Giant Array for Neutrino Detection (GRAND). The project aims at detecting ultra-high energy neutrinos with a 200,000 radio antenna array over 200,000\,km$^2$ as of the 2030s. With a fully transparent methodology based on open source data, we calculate the emissions related to three unavoidable sources: travel, digital technologies and hardware equipment. We find that these emission sources have a different impact depending on the stages of the experiment. Digital technologies and travel prevail for the small-scale prototyping phase (GRANDProto300), whereas hardware equipment (material production and transportation) and data transfer/storage largely outweigh the other emission sources in the large-scale phase (GRAND200k). In the mid-scale phase (GRAND10k), the three sources contribute equally. This study highlights the considerable carbon footprint of a large-scale astrophysics experiment, but also shows that there is room for improvement. We discuss various lines of actions that could be implemented. The GRAND project being still in its prototyping stage, our results provide guidance to the future collaborative practices and instrumental design in order to reduce its carbon footprint.