This cross-sectional study of 51 Mexican preschool children found that 68.6% had sleep disturbances after one year of COVID-19 confinement, with total sleep time averaging only 7 hours by actigraphy—well below the recommended 10–13 hours. Tablet use in the bedroom near bedtime was strongly associated with sleep disturbances (OR = 6.67), and children with higher sleep disturbance severity also showed significantly more emotional distress and behavioral difficulties. The findings highlight the need for age-tailored interventions targeting modifiable risk factors like bedtime electronics use.