Predicting the evolution of the brain network, also called connectome, by foreseeing changes in the connectivity weights linking pairs of anatomical regions makes it possible to spot connectivity-related neurological disorders in earlier stages and detect the development of potential connectomic anomalies. Remarkably, such a challenging prediction problem remains least explored in the predictive connectomics literature. It is a known fact that machine learning (ML) methods have proven their predictive abilities in a wide variety of computer vision problems. However, ML techniques specifically tailored for the prediction of brain connectivity evolution trajectory from a single timepoint are almost absent. To fill this gap, we organized a Kaggle competition where 20 competing teams designed advanced machine learning pipelines for predicting the brain connectivity evolution from a single timepoint. The competing teams developed their ML pipelines with a combination of data pre-processing, dimensionality reduction, and learning methods. Utilizing an inclusive evaluation approach, we ranked the methods based on two complementary evaluation metrics (mean absolute error (MAE) and Pearson Correlation Coefficient (PCC)) and their performances using different training and testing data perturbation strategies (single random split and cross-validation). The final rank was calculated using the rank product for each competing team across all evaluation measures and validation strategies. In support of open science, the developed 20 ML pipelines along with the connectomic dataset are made available on GitHub. The outcomes of this competition are anticipated to lead to the further development of predictive models that can foresee the evolution of brain connectivity over time, as well as other types of networks (e.g., genetic networks).