In the last five decades, iterative phase retrieval methods have drawn a lot of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement. However, in cases where a unique solution does exist, these methods often require oversampling and high computational resources, which limit the use of this approach in important applications. On the other hand, phase contrast methods are based on a single camera exposure, but provide only a qualitative description of the phase; thus, they are not useful for applications in which the quantitative phase description is needed. In this Letter, we establish a combined approach based on the two above-mentioned methods to overcome their respective drawbacks. We show that a modified phase retrieval algorithm easily converges to the correct solution by initializing the algorithm with a phase-induced intensity measurement, namely with a phase contrast image of the examined object. Accurate quantitative phase measurements for both binary and continuously varying phase objects are demonstrated to support the suggested system as a single-shot quantitative phase contrast microscope.