English-speaking adults often recruit a "mental timeline" to represent events from left-to-right (LR), but its developmental origins are debated. Here, we test whether preschoolers prefer ordered linear representations of events and whether they prefer culturally conventional directions. English-speaking adults (n = 85) and 3- to 5-year-olds (n = 513; 50% female; ~47% white, ~35% Latinx, ~18% other; tested 2016-2018) were told three-step stories and asked to choose which of two image sequences best illustrated them. We found that 3- and 4-year-olds chose ordered over unordered sequences, but preferences between directions did not emerge until at least age 5. Together, these results show that children conceptualize time linearly early in development but gradually acquire directional preferences (e.g., for LR).