Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit SWAP gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity (𝐹=100−6+0%) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to |⇓⇓⇓⟩, we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of μ𝑇2∗=12μs.