Observations of massive supermassive black holes (SMBHs) in the early Universe challenge existing black hole formation models. We propose that soliton cores in fuzzy dark matter (FDM) offer a potential solution to this timing problem. Our FDM cosmological zoom-in simulations confirm that, for a particle mass m_{FDM}∼10^{-22} eV, solitons are well developed at redshift z∼7 with masses of ∼10^{9}M_{⊙}, comparable to the observed SMBHs. We then demonstrate using hydrodynamic simulations that, compared to cold dark matter, these high-z massive FDM solitons with mass M_{s} can provide additional gravitational potential to accrete gas and boost the Bondi accretion rate of a growing black hole seed with mass M_{BH} by up to 2-4 orders of magnitude, in the regime of efficient cooling and negligible radiation pressure. This accretion boosting mechanism is effective for 10^{-22}≲m_{FDM}≲10^{-20} eV and potentially beyond as long as M_{s}>
M_{BH}.