Crystalline GeSn-on-insulator structures with high Sn concentration (>8%), which exceeds thermal equilibrium solid-solubility (similar to 2%) of Sn in Ge, are essential to achieve high-speed thin film transistors and high-efficiency optical devices. We investigate non-thermal equilibrium growth of Ge1-xSnx (0 <= x <= 0.2) on quartz substrates by using pulsed laser annealing (PLA). The window of laser fluence enabling complete crystallization without film ablation is drastically expanded (similar to 5 times) by Sn doping above 5% into Ge. Substitutional Sn concentration in grown layers is found to be increased with decreasing irradiation pulse number. This phenomenon can be explained on the basis of significant thermal non-equilibrium growth achieved by higher cooling rate after PLA with a lower pulse number. As a result, GeSn crystals with substitutional Sn concentration of similar to 12% are realized at pulse irradiation of single shot for the samples with the initial Sn concentration of 15%. Raman spectroscopy and electron microscopy measurements reveal the high quality of the grown layer. This technique will be useful to fabricate high-speed thin film transistors and high-efficiency optical devices on insulating substrates. Published by AIP Publishing.