Graph Neural Networks (GNNs) are proven to be a powerful machinery for learning complex dependencies in multivariate spatio-temporal processes. However, most existing GNNs have inherently static architectures, and as a result, do not explicitly account for time dependencies of the encoded knowledge and are limited in their ability to simultaneously infer latent time-conditioned relations among entities. We postulate that such hidden time-conditioned properties may be captured by the tools of multipersistence, i.e, a emerging machinery in topological data analysis which allows us to quantify dynamics of the data shape along multiple geometric dimensions. We make the first step toward integrating the two rising research directions, that is, time-aware deep learning and multipersistence, and propose a new model, Time-Aware Multipersistence Spatio-Supra Graph Convolutional Network (TAMP-S2GCNets). We summarize inherent time-conditioned topological properties of the data as time-aware multipersistence Euler-Poincar\'e surface and prove its stability. We then construct a supragraph convolution module which simultaneously accounts for the extracted intra- and inter- spatio-temporal dependencies in the data. Our extensive experiments on highway traffic flow, Ethereum token prices, and COVID-19 hospitalizations demonstrate that TAMP-S2GCNets outperforms the state-of-the-art tools in multivariate time series forecasting tasks.