After training on large datasets, certain deep neural networks are surprisingly good models of the neural mechanisms of adult primate visual object recognition. Nevertheless, these models are considered poor models of the development of the visual system because they posit millions of sequential, precisely coordinated synaptic updates, each based on a labeled image. While ongoing research is pursuing the use of unsupervised proxies for labels, we here explore a complementary strategy of reducing the required number of supervised synaptic updates to produce an adult-like ventral visual stream (as judged by the match to V1, V2, V4, IT, and behavior). Such models might require less precise machinery and energy expenditure to coordinate these updates and would thus move us closer to viable neuroscientific hypotheses about how the visual system wires itself up. Relative to standard model training on labeled images in ImageNet, we here demonstrate that the total number of supervised weight updates can be substantially reduced using three complementary strategies: First, we find that only 2% of supervised updates (epochs and images) are needed to achieve 80% of the match to adult ventral stream. Specifically, training benefits predictions of higher visual cortex the most whereas early visual cortex predictions only improve marginally over the course of training. Second, by improving the random distribution of synaptic connectivity, we find that 54% of the brain match can already be achieved “at birth" (i.e. no training at all). Third, we find that, by training only 5% of model synapses, we can still achieve nearly 80% of the match to the ventral stream. This approach further improves on ImageNet performance over previous attempts in computer vision of minimizing trained components without substantially increasing the relative number of trained parameters. These results reflect first steps in modeling not just primate adult visual processing during inference, but also how the ventral visual stream might be "wired up" by evolution (a model's "birth" state) and by developmental learning (a model's updates based on visual experience).