Reconstructions of the spatiotemporal dynamics of human dispersal away from evolutionary origins in Africa are important for determining the ecological consequences of the arrival of anatomically modern humans in naïve landscapes and interpreting inferences from ancient genomes on indigenous population history. While efforts have been made to independently validate these projections against the archaeological record and contemporary measures of genetic diversity, there has been no comprehensive assessment of how parameter values and choice of palaeoclimate model affect projections of early human migration. We simulated human migration into North America with a process-explicit migration model using simulated palaeoclimate data from two different atmosphere-ocean general circulation models and did a sensitivity analysis on the outputs using a machine learning algorithm. We found that simulated human migration into North America was more sensitive to uncertainty in demographic parameters than choice of atmosphere-ocean general circulation model used for simulating climate-human interactions. Our findings indicate that the accuracy of process-explicit human migration models will be improved with further research on the population dynamics of ancient humans, and that uncertainties in model parameters must be considered in estimates of the timing and rate of human colonisation and their consequence on biodiversity.