In many countries, in situ agricultural data is not available and cost-prohibitive to obtain. While remote sensing provides a unique opportunity to map agricultural areas and management characteristics, major efforts are needed to expand our understanding of cropping patterns and the potential for remotely monitoring crop production because this could support predictions of food shortages and improve resource allocation. In this study, we demonstrate a new method to map paddy rice using Google Earth Engine (GEE) and the Landsat archive in Bangladesh during the dry (boro) season. Using GEE and Landsat, dry-season rice areas were mapped at 30 m resolution for approximately 90,000 km2 annually between 2014 and 2018. The method first reconstructs spectral vegetation indices (VIs) for individual pixels using a harmonic time series (HTS) model to minimize the effect of any sensor inconsistencies and atmospheric noise, and then combines the time series indices with a rule-based algorithm to identify characteristics of rice phenology to classify rice pixels. To our knowledge, this is the first time an annual pixel-based time series model has been applied to Landsat at the national level in a multiyear analysis of rice. Findings suggest that the harmonic-time-series-based vegetation indices (HTS-VIs) model has the potential to map rice production across fragmented landscapes and heterogeneous production practices with comparable results to other estimates, but without local management or in situ information as inputs. The HTS-VIs model identified 4.285, 4.425, 4.645, 4.117, and 4.407 million rice-producing hectares for 2014, 2015, 2016, 2017, and 2018, respectively, which correlates well with national and district estimates from official sources at an average R-squared of 0.8. Moreover, accuracy assessment with independent validation locations resulted in an overall accuracy of 91% and a kappa coefficient of 0.83 for the boro/non-boro stable rice map from 2014 to 2018. We conclude with a discussion of potential improvements and future research pathways for this approach to spatiotemporal mapping of rice in heterogeneous landscapes.