First Three Act of 2021 This bill requires the Advanced Manufacturing Office of the Department of Energy to establish a program to provide grants or loan guarantees for certain innovative technology projects at industrial plants. The technology must (1) be technically viable at pilot scale and ready for commercial-scale implementation, (2) be able to reduce the energy use or greenhouse gas emissions, and (3) have the potential to reduce annual U.S. industrial energy use or greenhouse gas emissions by at least 1% once the technology is fully implemented at appropriate industrial plants in the United States.