The timeline of early lunar bombardment remains unclear. The bombardment rate as a function of time is commonly classified into three types of shapes: tail-end, sawtooth and terminal cataclysm. Differently-aged melt records the occurrence time of impact events and thus is crucial for constraining the timeline of early lunar bombardment. Based on a spatially resolved numerical model, we simulate the evolving distribution of differently-aged melt with a long-term impact mixing, where different shapes of impact rate function are considered. We compare the outcome of melt composition from different scenarios with the actual data from the lunar meteorites and the returned samples. The results suggest that, if the present actual data is representative of the melt composition on the Moon, the shape of the impact rate function is more likely comparable with the tail-end over the sawtooth and the terminal cataclysm, where the terminal cataclysm is least likely. In addition, using the state-of-the-art U-Pb dating techniques, more abundant ancient basin melt could be found in the returned samples.