We study the evolution of newborn neutron stars in high-mass X-ray binaries interacting with a wind-fed super-Eddington disk. The inner disk is regularized to a radiation-dominated quasi-spherical configuration for which we calculate the inner radius of the disk, the total luminosity of the system and the torque acting on the neutron star accordingly, following the evolution of the system through the ejector and early propeller stages. We find that the systems with B greater than or similar to 10(13) G pass through a short (similar to 20 yr) ejector stage appearing as supernova impostors followed by a propeller stage lasting similar to 10(3) yr. In the super-critical propeller stage the system is still bright (L similar to 10(40) erg s(-1)) due to the spindown power and therefore appears as an ultra-luminous X-ray source (ULX). The system evolves into pulsating ULX (PULX) when the neutron star spins down to a period (P similar to 1 s) allowing for accretion onto its surface to commence. Systems with lower magnetic fields, B similar to 10(11) G, pass through a long (10(5) yr) super-critical propeller stage with luminosities similar to those of the ultra-luminous super-soft sources (ULS), L less than or similar to 10(40) erg s(-1). The equilibrium periods of these systems in the accretion stage is about 10 ms, which is much smaller than the typical period range of PULX observed to date. Such systems could have a larger population, but their pulsations would be elusive due to the smaller size of the magnetosphere. Our results suggest that the ULS and some nonpulsating ULX are rapidly spinning and highly magnetized young neutron stars at the super-critical propeller stage.