We compare the abundant prolate shaped galaxies reported in deep JWST surveys, with the predicted stellar appearance of young galaxies in detailed hydro-simulations of three main dark matter contenders: Cold (CDM), Wave/Fuzzy ($\psi$DM) and Warm Dark Matter (WDM). The observed galaxy images closely resemble the elongated stellar appearance of young galaxies predicted by $\psi$DM and WDM, during the first $\simeq$ 500Myr when material steadily accretes along smooth filaments. The dark matter halos of WDM and $\psi$DM also have pronounced, prolate elongation similar to the stars, indicating a shared, highly triaxial equilibrium. This is unlike CDM where the early stellar morphology is mainly spheroidal, formed from fragmented filaments with frequent merging, resulting in modest triaxiality. Quantitatively, the excess of prolate galaxies observed by JWST matches well WDM and $\psi$DM for particle masses of 1.4 keV and $2.5\times 10^{-22}$ eV respectively. For CDM, several visible subhalos are typically predicted to orbit within the virial radius of each galaxy, whereas sub-halos are absent for WDM and $\psi$DM, as early merging is rare. We also find that $\psi$DM is distinguishable from WDM by the form of the core, which is predicted to be smooth and centered for WDM but is a dense soliton for $\psi$DM and typically offset from the galaxy center by wave perturbations. We emphasise the long, smooth filaments of $\psi$DM and WDM may be detectable with JWST, traced by stars and gas with comoving lengths of 150kpc predicted at z$\simeq$10, depending on the DM particle mass.