One of the leading models for the formation of multiple stellar populations within globular clusters is the "Fast Rotating Massive Star" (FRMS) scenario, where the ejecta of rapidly rotating massive stars is mixed with primordial material left over from the star-formation process, to form a second generation of stars within the decretion discs of the high mass stars. A requirement of this model, at least in its current form, is that young massive (i.e. proto-globular) clusters are not able to eject the unused gas and dust from the star-formation process from the cluster for 20-30 Myr after the formation of the first generation of stars, i.e. the cluster remains embedded within the gas cloud in which it forms. Here, we test this prediction by performing a literature search for young massive clusters in nearby galaxies, which have ages less than 20 Myr that are not embedded. We report that a number of such clusters exist, with masses near, or significantly above 10^6 Msun, with ages between a few Myr and ~15 Myr, suggesting that even high mass clusters are able to clear any natal gas within them within a few Myr after formation. Additionally, one cluster, Cluster 23 in ESO~338-IG04, has a metallicity below that of some Galactic globular clusters that have been found to host multiple stellar populations, mitigating any potential effect of differences in metallicity in the comparison. The clusters reported here are in contradiction to the expectations of the FRMS scenario, at least in its current form. ; Comment: 8 pages, 4 figures, accepted for publication in MNRAS