Using recently acquired Hubble Space Telescope NIR observations (J, Pa{beta}, and H bands) of the nearby galaxy NGC 1313, we investigate the timescales required by a young star cluster to emerge from its natal cloud. We search for extincted star clusters, potentially embedded in their natal cloud as either (1) compact sources in regions with high H{alpha}/Pa{beta} extinctions or (2) compact HII regions that appear as point-like sources in the Pa{beta} emission map. The NUV-optical-NIR photometry of the candidate clusters is used to derive their ages, masses, and extinctions via a least-{chi}^2^ spectral energy distribution broad- and narrowband fitting process. The 100 clusters in the final samples have masses in the range log_10_(M/M_{sun}_)=2.5-3.5 and moderate extinctions, E(B-V)<~1.0mag. Focusing on the young clusters (0-6Myr), we derive a weak correlation between extinction and age of the clusters. Almost half of the clusters have low extinctions, E(B-V)<0.25mag, already at very young ages (<=3Myr), suggesting that dust is quickly removed from clusters. A stronger correlation is found between the morphology of the nebular emission (compact, partial or absent, both in H{alpha} and Pa{beta}) and cluster age. Relative fractions of clusters associated with a specific nebular morphology are used to estimate the typical timescales for clearing the natal gas cloud, resulting in between 3 and 5Myr, ~1Myr older than what was estimated from NUV-optical-based cluster studies. This difference hints at a bias for optical-only-based studies, which James Webb Space Telescope will address in the coming years.