  Here we perform angle and time-resolved photoelectron spectroscopy on the
commensurate Charge Density Wave (CDW) phase of 1T-TaS$_2$. Data with different
probe pulse polarization are employed to map the dispersion of electronic
states below and above the chemical potential. Upon photoexcitation, the
fluctuations of CDW order erase the band dispersion near to the chemical
potential and halve the charge gap size. This transient phase sets within half
a period of the coherent lattice motion and is favored by strong electronic
correlations. The experimental results are compared to Density-Functional
Theory (DFT) calculations with a self-consistent evaluation of the Coulomb
repulsion. Our simulations indicate that the screening of Coulomb repulsion
depends on the stacking order of the TaS$_2$ layers. The entanglement of such
degrees of freedom suggest that both the structural order and electronic
repulsion are locally modified by the photoinduced CDW fluctuations.
