Currently, the game offers a bevy of policies and decisions that effect the Strong Leader and Compassionate Perceptions, but peculiarly only policy flip flops and corruption influence your Trustworthyness, meaning it can only ever get to 10% without stunts.
Perhaps the Human Development and Equality simulations should have an effect, or perhaps the Right to Privacy or Consumer Rights policies could. Worker satisfaction doesn’t have a simulation, but I’d think mandating Workers on Boards or similar policies might compel those workers to trust your government in turn?