The agricultural sector’s progress toward climate neutrality is of great importance not only in the climate, but also in economic and social contexts. Climate-neutral agriculture is highly dependent on innovations that ensure maximum efficient farming, which not only reduces emissions but also ensures competitiveness in the market; all of this is fundamentally influenced by well-considered policies. Due to the complicated structure of the sector, it tends to be very difficult or even impossible to determine the real obstacles that delay the progress of sustainable farming. Therefore, this research aims to create a system dynamics model using Latvia as a case study, which would not only provide an insight into the system’s structure, but also identify the system’s weak links and allow for the development of recommendations. The model can calculate not only the generated emissions per unit of production, but also the investments required to reduce 1 kt of CO2eq generated, and results could help policymakers in any country to make rational, non-controversial decisions simultaneously in the context of economic and Green Deal objectives. The results of the study demonstrate that to increase economic competitiveness and reduce emissions in agriculture, the most important aspect is the ability to invest in innovations and new technologies that would achieve not only the lowest emissions, but also high productivity and competitiveness in the market. The research shows that the strategic documents emphasize manure management and improvement of feed quality, but there is an important element missing—an emphasis on thermoregulation improvements for animals. By improving feed quality, manure management, and thermoregulation all together, there was a 60% GHG emission reduction without reducing—and even significantly increasing—milk yield. In addition, in a comprehensive improvement of the new innovations, the case study company managed to increase milk yield by 69%.