Trillion Trees Act This bills establishes a variety of requirements and incentives to plant trees and conduct other land management practices for the purposes of capturing and storing carbon in domestic and international trees and forests. Additionally, the bill provides incentives to research or develop other carbon sequestration tools. Specifically, the bill directs the Department of Agriculture (USDA) to set targets to increase forest carbon stock through January 1, 2100, for the purposes of sequestering and storing carbon in U.S. forests. It also establishes and provides funding for the Trillion Trees Challenge Fund to provide grants to nonfederal entities for activities related to reforestation efforts on public or private lands. In addition, it raises the cap on the Reforestation Trust Fund to enhance forest health in the National Forest System and requires the USDA to establish a Tree City USA Grant Program. The bill also allows the U.S. Agency for International Development to enter into an agreement with a nonprofit organization to establish an International Forest Foundation to promote reforestation and prevent deforestation. Additionally, it establishes requirements and incentives to address seedling shortages and support nurseries. Finally, the bill provides market incentives to research or develop other carbon sequestration tools relating to biochar, sustainable building practices, biochemical and bioplastic products, and biomass energy.