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Using recently acquired HST NIR observations (J, Pa$β$ and H bands) of the nearby galaxy NGC1313, 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$α$/Pa$β$ extinctions; 2. compact HII regions that appear as point-like sources in the Pa$β$ emission map. The NUV--optical--NIR photometry of the candidate clusters is used to derive their ages, masses and extinctions via a least$-χ^2$ SED broad and narrow--band fitting process. The 100 clusters in the final samples have masses in the range $\rm \log_{10}(M/M_\odot)=2.5-3.5$ and moderate extinctions, $\rm E(B-V)\lesssim1.0$ mag. Focusing on the young clusters ($0-6$ Myr) we derive a weak correlation between extinction and age of the clusters. Almost half of the clusters have low extinctions, $\rm E(B-V)<0.25$ mag, already at very young ages ($\le3$ Myr), 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$α$ and Pa$β$) and cluster age. Relative fractions of clusters associated with a specific nebular morphology is used to estimate the typical timescales for clearing the natal gas cloud, resulting between 3 and 5 Myr, $\sim1$ Myr older than what estimated from NUV--optical--based cluster studies. This difference hints to a bias for optically--only based studies, which JWST will address in the coming years.