Quantitative Susceptibility Mapping (QSM) is a technique that derives tissue magnetic susceptibility distributions from phase measurements obtained through Magnetic Resonance (MR) imaging. This involves solving an ill-posed dipole inversion problem, however, and thus time-consuming and cumbersome data acquisition from several distinct head orientations becomes necessary to obtain an accurate solution. Most recent (supervised) deep learning methods for single-phase QSM require training data obtained via multiple orientations. In this work, we present an alternative unsupervised learning approach that can efficiently train on single-orientation measurement data alone, named ProxiMO (Proximal Multi-Operator), combining Learned Proximal Convolutional Neural Networks (LP-CNN) with multi-operator imaging (MOI). This integration enables LP-CNN training for QSM on single-phase data without ground truth reconstructions. We further introduce a semi-supervised variant, which further boosts the reconstruction performance, compared to the traditional supervised fashions. Extensive experiments on multi-center datasets illustrate the advantage of unsupervised training and the superiority of the proposed approach for QSM reconstruction. Code is available at https://github.com/shmuelor/ProxiMO