The overabundance of super-early (redshift $z>10$) luminous ($M_ UV < -20$) blue galaxies detected by JWST has been explained as being due to negligible dust attenuation in these systems. We show that this model correctly reproduces the UV luminosity function at $z>10$ and the star formation rate (SFR) density evolution. The model also predicts, in agreement with data, that the cosmic specific SFR (sSFR) grows as $ sSFR $. At $z 10$, the cosmic sSFR crosses the critical value $ sSFR^ $, and approximately $45$<!PCT!> of the galaxies become super-Eddington, driving outflows reaching velocities of $ where $ and $f_M$ are the star formation efficiency and fraction of the halo gas expelled in the outflow, respectively. This prediction is consistent with the outflow velocities measured in 12 super-Eddington galaxies of the JWST /JADES sample. Such outflows clear the dust, thus boosting the galaxy luminosity. They also dramatically enhance the visibility of the Lyalpha line from $z>10$ galaxies by introducing a velocity offset. The observed Lyalpha properties in GN-z11 ($z=10.6$) are simultaneously recovered by the outflow model if $ HI 20.1$, implying that the outflow is largely ionized. We make analogous predictions for the Lyalpha visibility of other super-early galaxies, and we compare the model with Lyalpha surveys at $z>7$, finding that essentially all super-Eddington (sub-Eddington) galaxies are (not) detected in Lyalpha . Finally, the sSFR positively correlates with the LyC escape fraction, as outflows carve ionized transparent channels through which LyC photons leak.