Semi-supervised learning (SSL) in non-stationary environments has received relatively little attention in machine learning, despite a growing number of applications that can benefit from a properly configured SSL algorithm. Previous works in learning non-stationary data have analyzed such cases where both labeled and unlabeled instances are received at every time step and/or in regular intervals; however, to the best of our knowledge, no work has investigated the case where labeled instances are received only at the initial time step, followed by unlabeled instances provided in subsequent time steps. In this proof-of-concept work, we propose a new framework for learning in a non-stationary environment that provides only unlabeled data after the initial time step, to which we refer to as initially labeled environment. The proposed framework generates labels for previously unlabeled data at each time step to be combined with incoming unlabeled data - possibly from a drifting distribution - using a compacted polytope sample extraction algorithm. We have conducted two experiments to demonstrate the feasibility and reliability of the approach. This proof-of-concept is presented in two dimensions; however, the algorithm can be extended to higher dimensions with appropriate modifications.