Naturally Offsetting Emissions by Managing and Implementing Tillage Strategies Act of 2023 or the NO EMITS Act of 2023 This bill directs the Department of Agriculture (USDA) to carry out activities to improve soil health, including to address climate change. Specifically, USDA must establish a program that provides agricultural producers incentives (i.e., payments) for and technical assistance with adopting or maintaining practices or cropping systems to improve soil health, award grants to states and Indian tribes for implementing soil health programs, and use a portion of funds of the Commodity Credit Corporation to provide agricultural producers with technical assistance for mitigating and adapting to climate change. The bill also (1) makes practices related to livestock production eligible for certain competitive grants under the On-Farm Conservation Innovation Trials program, and (2) increases funding for the program.