We observed the W51 high-mass star-forming complex with ALMAs longest-baseline configurations, achieving an angular resolution of $sim$20 milliarcseconds, corresponding to a linear resolution of $sim$100 au at $D_{mathrm{W51}}=5.4$ kpc. The observed region contains three high-mass protostars in which the dust continuum emission at 1.3 mm is optically-thick up to a radius $lesssim$1000 au and has brightness temperatures $gtrsim$200 K. The high luminosity ($gtrsim10^4$ L$_{odot}$) in the absence of free-free emission suggests the presence of massive stars ($Mgtrsim20$ M$_{odot}$) at the earliest stages of their formation. Our continuum images reveal remarkably complex and filamentary structures arising from compact cores. Molecular emission shows no clear signs of rotation nor infall on scales from 150 to 2000 au: we do not detect disks. The central sources drive young ($sim$100 years), fast ($sim 100$ km s$^{-1}$), powerful ($dot{M}>10^{-4}$ M$_{odot} yr^{-1}$), collimated outflows. These outflows provide indirect evidence of accretion disks on scales $rlesssim$100--500 au (depending on the object). The active outflows are connected to fossil flows that have different orientations on larger spatial scales, implying that the orientations of these small disks change over time. These results together support a variant of an accretion model for high-mass star formation in which massive protostars do not form a large, stable Keplerian disk during their early stages, but instead they accrete material from multiple massive flows with different angular momentum vectors. This scenario therefore contrasts with the simplified classic paradigm of a stable disk+jet system, which is the standard model for low-mass star formation, and provides an experimental confirmation of a multi-directional and unsteady accretion model for massive star formation.