Dengue is a vector-borne disease transmitted to humans by vectors of genus Aedes causing a global threat to health, social, and economic sectors in many of the tropical countries including Sri Lanka. In Sri Lanka, the tropical climate, marked by seasonal weather primarily influenced by monsoons, fosters optimal conditions for the virus to spread efficiently, especially during monsoon periods. This heightened transmission results in increased per-capita vector density. In this work, we investigate the dynamic influence of environmental conditions on dengue emergence in Colombo district- the geographical region with the highest recorded dengue threat in Sri Lanka. An iterative approach is employed to estimate dengue cases dynamically leveraging the Markov chain Monte Carlo simulations, utilizing the dynamics of weather patterns governing in the region. The developed algorithm allows to estimate the risk of dengue outbreaks with high precision, facilitating accurate forecasts of upcoming disease emergence patterns for better preparedness. The uncertainty quantification not only validated the accuracy of outbreak estimates but also showcased the model's capacity to capture extreme cases and revealed undisclosed external factors that might affect dengue transmission.