Significance Our laser-plasma experiment has reproduced the physical process thought to be responsible for generating and sustaining magnetic fields in turbulent plasmas (the “fluctuation dynamo”), and has accessed the viscosity-dominated regime of relevance to most of the plasma in the universe. These measurements are also time resolved, which provides evolutionary information about the fluctuation dynamo (including the field’s growth rate) previously available only from simulations. The efficient amplification of large-scale magnetic fields seen in our experiment could explain the origin of large-scale fields that are observed in turbulent astrophysical plasmas, but are not predicted by current analytical calculations or idealized simulations of the fluctuation dynamo.