The world's ecosystem and environment are rapidly deteriorating with an increase in the depletion of forest conditions due to forest fires. In recent past years, wildfire incidents in Sikkim have increased due to severe climatic changes such as turbulent rainfall, untimely summers, extreme droughts in winters, and a reduction in the percentage of yearly rainfall. Forest fires are one of the numerous kinds of disasters that impose disastrous changes on the entire environment and disrupt the complex correspondence of the flora and fauna. The research's goal is to examine the vegetation indices based on different climates to know why forest vegetation is decreasing day by day from 2000 to 2023. The frequent changes in forest vegetation are extensively studied by using satellite images. This data has been collected by three satellites Landsat-5, Landsat-8, and Landsat-9 on different vegetation indices NDVI, EVI, and NDWI. East Sikkim area is chosen to compute forest vegetation indices based on the heap's landmass this region is unexplored yet and also studied about the forest changes by using different spatial temporal indices in the range of the entire district in the future. The authors of this paper have used Landsat multi-spectral data to assess changes in the area of vegetation in a sub-tropical region like a dense forest region in east Sikkim. The analysis depicts space images, computes vegetation indices (NDVI, EVI, NDWI), and accomplishes mathematical computation of findings. The proposed method will be helpful to discuss the variance of vegetation in the entire East Sikkim region at the time span of 2000-2023. In the analysis, we find that mean and standard deviation values change over the years in all indices. Later, we also calculated changes by using a classification model and find a total 10% change in forest areas in approximately 22 years.