Sustaining Our Democracy Act This bill establishes and provides funds through FY2032 for the State Election Assistance and Innovation Trust Fund for purposes of promoting election activities. Specifically, the bill establishes the Democracy Advancement and Innovation Program, through which the Office of Democracy Advancement and Innovation (also established by this bill) shall make allocations to states for carrying out democracy promotion activities. These activities include improving the administration of federal elections, recruiting and training nonpartisan election officials and poll workers, and increasing voting access. The bill requires each state, in order to receive allocated funds, to (1) submit a plan for approval that describes how the state will distribute resources and carry out democracy promotion activities, and (2) establish uniform and nondiscriminatory state-based administrative complaint procedures. The bill prohibits states from using funds for certain activities, including any activity that diminishes the ability of any eligible voter to participate in the electoral process.