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Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effect of initial density fluctuations on cumulants of the net-proton multiplicity distribution in Au + Au Collisions at s N N = 7.7 GeV was investigated by varying the minimum distance d min between two nucleons in the initialization. It was found that the initial density fluctuations increased with the decrease of d min from 1.6 fm to 1.0 fm, and the influence of d min on the magnitude of the net-proton number fluctuation in a narrow pseudorapidity window ( Δ η ≤ 4) was negligible even if it indeed affected the density evolution during the collision. At a broad pseudorapidity window ( Δ η ≥ 4), the cumulant ratios were enlarged when the initial density fluctuations were increased with the smaller value of d min , and this enhancement was comparable to that observed in the presence of the nuclear mean-field potential. Moreover, the enhanced cumulants were more evident in collisions with a larger impact parameter. The present work demonstrates that the fingerprint of the initial density fluctuations on the cumulants in a broad pseudorapidity window is clearly visible, while it is not obvious as the pseudorapidity window becomes narrow. [ABSTRACT FROM AUTHOR]