We investigate the hypothesis that spacetime is not a fundamental entity but emerges from underlying quantum fields and matter. Motivated by the field-based nature of atomic structure, where apparent empty space is governed by quantum probability distributions, we propose a wave--spacetime correspondence in which geometry arises from field gradients. In this framework, gravity is interpreted as a macroscopic manifestation of collective wave dynamics rather than an independent interaction. To test this idea, we analyze Planck SMICA temperature and polarization data, examining Gaussianity, hemispherical asymmetry, phase correlations, bispectrum, and B-mode power. The observed phase correlation ($\sim 0.21$), bispectrum amplitude ($\sim 10^{-20}$), and polarization asymmetry ($\sim 10^{-2}$) are all consistent with a Gaussian random field. A weak hemispherical asymmetry is detected at large scales ($A \approx 0.058$, $\sim 1.6\sigma$), but shows no significant scale dependence or polarization support. No detectable B-mode signal beyond noise is observed. These results indicate that large-scale cosmological fluctuations are well described by linear Gaussian dynamics, placing constraints on emergent spacetime models. Any wave--spacetime coupling must be weak or confined to early-universe regimes. The proposed framework provides a unified conceptual description of spacetime and quantum fields, while remaining consistent with current observational limits.