There has never been a cryogenic rocket stage to fire outside of earth’s gravitational influence. This is primarily driven by a mass/volume trade-off of insulation and active refrigeration which directly dictates coast phase timing due to LH2 boil-off.
Humanity’s most efficient chemical and nuclear space-stage rockets are fueled by hydrogen. Yet, novel system-level Cryogenic Fluid Management (CFM) is needed to be a ubiquitous fuel used for space transport.
B Pedrow “Parahydrogen-Orthohydrogen Conversion on Catalyst Loaded Scrim for Vapor Cooled Shielding of Cryogenic Storage Vessels” School of Mechanical and Materials Engineering, Washington State University, 2016.