Trillion Trees and Natural Carbon Storage Act This bill directs the Department of Agriculture (USDA), in collaboration with the National Oceanic and Atmospheric Administration, to establish (1) objectives for increased net carbon stock for the forest, grassland, wetland, and coastal blue carbon habitat ecosystems of the United States that are owned or managed by the federal government; and (2) objectives that shall be developed collaboratively between one or more nonfederal entities and one or more federal partners for increased net carbon stock for the forest, grassland, wetland, and coastal blue carbon habitat ecosystems of the United States that are owned or managed by a state or local government, an Indian Tribe, or a private person. USDA shall establish a program, to be known as the Rural Forest Market Investment Program, to guarantee an environmental impact bond, loan, or other investment vehicle issued for the sole purpose of financing eligible projects developed to facilitate the sale of credits in the voluntary carbon market or other recognized environmental market to enable rural private forest landowners to participate in an innovative market for forest carbon or other products. USDA may enter into an agreement, or expand on existing partnerships, with a nonprofit organization to establish an International Forest Foundation to, among other things, support forest landscape restoration, end deforestation, and conserve and restore grasslands, wetlands, and blue carbon habitats around the world.