We present Branas-TIDE, an effective open-brane cosmological framework in which the observable Universe is modeled as a four-dimensional brane embedded in a higher-dimensional bulk. In this setting, global energy conservation is preserved in the bulk, while effective mass–energy exchange is allowed on the brane, leading to observable late-time interaction effects. The framework is motivated by recent observational tensions within ΛCDM, including discrepancies in the expansion history and the unexpectedly early emergence of chemically mature and structurally developed galaxies at high redshift. Rather than introducing new particle species, Branas-TIDE interprets dark matter– and dark energy–like phenomena as effective manifestations of inherited curvature and residual inflow from a parent environment. We explore the qualitative observational implications of this open-system approach through simplified numerical experiments, including tests of the expansion history, large-scale structure consistency, and early chemical evolution. In particular, the model predicts a non-vanishing chemical floor at extreme redshift and mild small-scale structural enhancement, providing clear and falsifiable signatures for current and upcoming JWST and large-scale survey data. Branas-TIDE is presented as a phenomenological and internally consistent framework rather than a precision cosmological model. Supplementary code and exploratory analyses supporting transparency and reproducibility are provided alongside the manuscript.