X-ray binaries are stellar systems composed of a compact object (either a stellar-mass black hole or a neutron star) and a donor star that transfers mass to the former. Outflows represent fundamental physical phenomena to understand accretion processes in these systems. Black holes show three types of outflows: radio-jets and optical winds during the hard accretion states, and highly ionised winds observed in X-rays during the soft states. The black hole transient MAXI J1820+070 showed optical winds with velocities up to 1800 km/s during the hard state of its 2018-2019 outburst. In this work we present the discovery of infrared winds that are present throughout the entire outburst of the black hole, that is, during both hard and soft states. This represents the first detection of a state-independent wind in a black hole transient. Furthermore, this near-infrared wind shows similar kinetic properties to the optical one, suggesting that we are observing the same wind, whose visibility varies as a function of the accretion state. This discovery represents a new milestone in our understanding of accretion and its associated outflows in stellar-mass black holes.