We propose a new mechanism for the growth of supermassive black hole (BH) seeds in the star-forming progenitors of local early-type galaxies (ETGs) at $zgtrsim 1$. This envisages the migration and merging of stellar compact remnants (neutron stars and stellar-mass BHs) via gaseous dynamical friction toward the central high-density regions of such galaxies. We show that, under reasonable assumptions and initial conditions, the process can build up central BH masses of order $10^4-10^6, M_odot$ within some $10^7$ yr, so effectively providing heavy seeds before standard disk (Eddington-like) accretion takes over to become the dominant process for further BH growth. Remarkably, such a mechanism may provide an explanation, alternative to super-Eddington accretion rates, for the buildup of billion solar masses BHs in quasar hosts at $zgtrsim 7$, when the age of the Universe $lesssim 0.8$ Gyr constitutes a demanding constraint; moreover, in more common ETG progenitors at redshift $zsim 2-6$ it can concur with disk accretion to build such large BH masses even at moderate Eddington ratios $lesssim 0.3$ within the short star-formation duration $lesssim$ Gyr of these systems. Finally, we investigate the perspectives to detect the merger events between the migrating stellar remnants and the accumulating central supermassive BH via gravitational wave emission with future ground and space-based detectors such as the Einstein Telescope (ET) and the Laser Interferometer Space Antenna (LISA).
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