The high-energy universe has revealed that energetic particles are ubiquitous in the cosmos and play a vital role in the cultivation of cosmic environments on all scales. Our pursuit of more than a century to uncover the origins and fate of these cosmic energetic particles has given rise to some of the most interesting and challenging questions in astrophysics. Energetic particles in our own galaxy, galactic cosmic rays (GCRs), engage in a complex interplay with the interstellar medium and magnetic fields in the galaxy, giving rise to many of its key characteristics. For instance, GCRs act in concert with galactic magnetic fields to support its disk against its own weight. GCR ionization and heating are essential ingredients in promoting and regulating the formation of stars and protostellar disks. GCR ionization also drives astrochemistry, leading to the build up of complex molecules in the interstellar medium. GCR transport throughout the galaxy generates and maintains turbulence in the interstellar medium, alters its multi-phase structure, and amplifies magnetic fields. GCRs could even launch galactic winds that enrich the circumgalactic medium and alter the structure and evolution of galactic disks. As crucial as they are for many of the varied phenomena in our galaxy, there is still much we do not understand about GCRs. While they have been linked to supernova remnants (SNRs), it remains unclear whether these objects can fully account for their entire population, particularly at the lower (approximately less than 1 GeV per nucleon) and higher (~PeV) ends of the spectrum. In fact, it is entirely possible that the SNRs that have been found to accelerate CRs merely re-accelerate them, leaving the origins of the original GCRs a mystery. The conditions for particle acceleration that make SNRs compelling source candidates are also likely to be present in sources such as protostellar jets, superbubbles, and colliding wind binaries (CWBs), but we have yet to ascertain their roles in producing GCRs. For that matter, key details of diffusive shock acceleration (DSA) have yet to be revealed, and it remains to be seen whether DSA can adequately explain particle acceleration in the cosmos. This White Paper is the first of a two-part series highlighting the most well-known high-energy cosmic accelerators and contributions that MeV gamma-ray astronomy will bring to understanding their energetic particle phenomena. For the case of GCRs, MeV astronomy will: 1) Search for fresh acceleration of GCRs in SNRs; 2) Test the DSA process, particularly in SNRs and CWBs; 3) Search for signs of CR acceleration in protostellar jets and superbubbles