Luminous quasars are powerful targets to investigate the role of feedback from supermassive black holes (BHs) in regulating the growth phases of BHs themselves and of their host galaxies, up to the highest redshifts. Here we investigate the cosmic evolution of the occurrence and kinematics of BH-driven outflows, as traced by broad absorption line (BAL) features, due to the C iv ionic transition. We exploit a sample of 1935 quasars at z = 2.1-6.6 with bolometric luminosity log(L (bol)/erg s(-1)) & GSIM; 46.5, drawn from the Sloan Digital Sky Survey and from the X-Shooter legacy survey of Quasars at the Reionization Epoch (XQR-30). We consider rest-frame optical bright quasars to minimize observational biases due to quasar selection criteria. We apply a homogeneous BAL-identification analysis, based on employing composite template spectra to estimate the quasar intrinsic emission. We find a BAL quasar fraction close to 20% at z & SIM; 2-4, while it increases to almost 50% at z & SIM; 6. The velocity and width of the BAL features also increase at z & GSIM; 4.5. We exclude the possibility that the redshift evolution of the BAL properties is due to differences in terms of quasar luminosity and accretion rate. These results suggest significant BH feedback occurring in the 1 Gyr old universe, likely affecting the growth of BHs and, possibly, of their host galaxies, as supported by models of early BH and galaxy evolution.