Previous evidence indicates trust is an important correlate of compliance with COVID-19 containment policies. However, this conclusion hinges on two crucial assumptions: first, that compliance does not change over time, and second, that mobility or self-reported measures are good proxies for compliance. This study is the first to use a time-varying measure of compliance to study the relationship between compliance and trust in others and institutions over the period from March 2020 to January 2021 in ten mostly European countries. We calculate a time-varying measure of compliance as the association between containment policies and people's mobility behavior using data from the Oxford Policy Tracker and Google. Additionally, we develop measures of trust in others and national institutions by applying emotion analysis to Twitter data. We test the predictive role of our trust measures using various panel estimation techniques. Our findings demonstrate that compliance does change over time and that increasing (decreasing) trust in others predicts increasing (decreasing) compliance. This evidence indicates compliance should not be taken for granted, and confirms the importance of cultivating trust in others. Nurturing trust in others, through ad-hoc policies such as community activity programs and urban design to facilitate social interactions, can foster compliance with public policies.