Better Utilizing Investments to Leverage Development and Generating Renewable Energy to Electrify the Nation's Infrastructure and Jobs Act or the BUILD GREEN Infrastructure and Jobs Act This bill directs the Department of Transportation (DOT) to establish a green transportation infrastructure program to provide competitive grants to states, local governments, and other entities for capital investments in electrified surface transportation infrastructure projects. DOT must select projects that maximize sustainability, including projects that (1) promote the electrification of all public transportation, (2) contribute to climate resilience and mitigation, (3) reduce air pollution and greenhouse gas emissions, and (4) achieve energy savings and reduce energy usage compared to other eligible projects. Additionally, DOT must prioritize projects that (1) serve a frontline, vulnerable, or disadvantaged community; (2) are located in an area that has experienced high adverse health and environmental impacts on minority and low-income populations; (3) require federal funds in order to complete an overall financing package; or (4) add a new green space or new state or local park units and outdoor recreational areas. Grants issued under the program may not be less than $2 million, with the exception of grants for project planning, preparation, or design, which are not subject to a minimum amount. The federal share of the cost of a project may not exceed 85% for planning, design, and construction purposes and 50% of the operation and maintenance costs of the project for its first 10 years.