Cosmological simulations like CAMELS and IllustrisTNG characterize hundreds of thousands of galaxies using various internal properties. Previous studies have demonstrated that machine learning can be used to infer the cosmological parameter Ωm from the internal properties of even a single randomly selected simulated galaxy. This ability was hypothesized to originate from galaxies occupying a low-dimensional manifold within a higher-dimensional galaxy property space, which shifts with variations in Ωm. In this work, we investigate how galaxies occupy the high-dimensional galaxy property space, particularly the effect of Ωm and other cosmological and astrophysical parameters on the putative manifold. We achieve this by using an autoencoder with an information-ordered bottleneck, a neural layer with adaptive compression, to perform dimensionality reduction on individual galaxy properties from CAMELS simulations, which are run with various combinations of cosmological and astrophysical parameters. We find that for an autoencoder trained on the fiducial set of parameters, the reconstruction error increases significantly when the test set deviates from fiducial values of Ωm and ASN1, indicating that these parameters shift galaxies off the fiducial manifold. In contrast, variations in other parameters such as σ8 cause negligible error changes, suggesting galaxies shift along the manifold. These findings provide direct evidence that the ability to infer Ωm from individual galaxies is tied to the way Ωm shifts the manifold. Physically, this implies that parameters like σ8 produce galaxy property changes resembling natural scatter, while parameters like Ωm and ASN1 create unsampled properties, extending beyond the natural scatter in the fiducial model.