This study presents bounds on transient variations of fundamental constants, with typical timescales ranging from minutes to months, using clocks in space. The underlying phenomenology describing such transient variations relies on models for Dark Matter (DM) which suggest possible encounters of macroscopic compact objects with the Earth, due to the motion of the solar system in the galactic halo. If such compact objects possess an effective feeble interaction with the ordinary matter beyond the gravitational one, it may result in effective transient variations of fundamental constants. Such variations leave signatures on clocks onboard GNSS satellites. In this paper, we introduce a phenomenological study dedicated to the search for such DM transient objects using the network of passive hydrogen masers (H-Masers) onboard Galileo satellites. We first model the signature of transient variations of fundamental constants as a frequency modulation in the difference between two satellite clocks, considering the satellite trajectories relative to the transient event. Then, we present first results based on a fast analysis method, the maximum reach analysis. The main result is a significant extension of the discovery range for DM transients, with a sensitivity never achieved before. We investigate indeed the range of transient sizes from $10^5$ to $10^9$ kilometres, which, apart from indirect and model-dependent non-transient effects, has never been explored previously.