In this work, we introduce Progressive Growing of Patch Size, an automatic curriculum learning approach for 3D medical image segmentation. Our approach progressively increases the patch size during model training, resulting in an improved class balance for smaller patch sizes and accelerated convergence of the training process. We evaluate our curriculum approach in two settings: a resource-efficient mode and a performance mode, both regarding Dice score performance and computational costs across 15 diverse and popular 3D medical image segmentation tasks. The resource-efficient mode matches the Dice score performance of the conventional constant patch size sampling baseline with a notable reduction in training time to only 44%. The performance mode improves upon constant patch size segmentation results, achieving a statistically significant relative mean performance gain of 1.28% in Dice Score. Remarkably, across all 15 tasks, our proposed performance mode manages to surpass the constant patch size baseline in Dice Score performance, while simultaneously reducing training time to only 89%. The benefits are particularly pronounced for highly imbalanced tasks such as lesion segmentation tasks. Rigorous experiments demonstrate that our performance mode not only improves mean segmentation performance but also reduces performance variance, yielding more trustworthy model comparison. Furthermore, our findings reveal that the proposed curriculum sampling is not tied to a specific architecture but represents a broadly applicable strategy that consistently boosts performance across diverse segmentation models, including UNet, UNETR, and SwinUNETR. In summary, we show that this simple yet elegant transformation on input data substantially improves both Dice Score performance and training runtime, while being compatible across diverse segmentation backbones.