At the temperatures and stresses associated with the onset of convection in an ice I shell of the Galilean satellites, ice behaves as a non-Newtonian fluid with a viscosity that depends on both temperature and strain rate. The convective stability of a non-Newtonian ice shell can be judged by comparing the Rayleigh number of the shell to a critical value. Previous studies suggest that the critical Rayleigh number for a non-Newtonian fluid depends on the initial conditions in the fluid layer, in addition to the thermal, rheological, and physical properties of the fluid. We seek to extend the existing definition of the critical Rayleigh number for a non-Newtonian, basally heated fluid by quantifying the conditions required to initiate convection in an ice I layer initially in conductive equilibrium. We find that the critical Rayleigh number for the onset of convection in ice I varies as a power (-0.6 to -0.5) of the amplitude of the initial temperature perturbation issued to the layer, when the amplitude of perturbation is less than the rheological temperature scale. For larger-amplitude perturbations, the critical Rayleigh number achieves a constant value. We characterize the critical Rayleigh number as a function of surface temperature of the satellite, melting temperature of ice, and rheological parameters so that our results may be extrapolated for use with other rheologies and for a generic large icy satellite. The values of critical Rayleigh number imply that triggering convection from a conductive equilibrium in a pure ice shell less than 100 km thick in Europa, Ganymede, or Callisto requires a large, localized temperature perturbation of a few kelvins to tens of kelvins to soften the ice and therefore may require tidal dissipation in the ice shell.