Optical phase estimation is a vital measurement strategy that is used to perform accurate measurements of various physical quantities including length, velocity and displacements(1,2). The precision of such measurements can be greatly enhanced by the use of entangled or squeezed states of light as demonstrated in a variety of different optical systems(3-8). Most of these accounts, however, deal with the measurement of a very small shift of an already known phase, which is in stark contrast to ab initio phase estimation where the initial phase is unknown(9-12). Here, we report on the realization of a quantum-enhanced and fully deterministic ab initio phase estimation protocol based on real-time feedback control. Using robust squeezed states of light combined with a real-time Bayesian adaptive estimation algorithm, we demonstrate deterministic phase estimation with a precision beyond the quantum shot noise limit. The demonstrated protocol opens up new opportunities for quantum microscopy, quantum metrology and quantum information processing.