The processes of nucleation and growth of methane hydrate in a highly supercooled two-phase "methane-water" system obtained using various cooling protocols are considered. It has been shown that, at sufficiently high cooling rates, crystalline forms of methane hydrate can still form in the system. It was found that, at a cooling rate of γ=1.0 K/ps, the process of nucleation and growth of gas hydrate was observed in all independent molecular dynamics iterations, while at a cooling rate of γ=10.0 K/ps, no nucleation event was observed in ~26.7% of numerical experiments. It was found that with an increase in the cooling rate of the system, an increase in the average time scale of nucleation tauc and a decrease in the critical size of the nucleus nc are observed. It is shown that at a sufficiently deep level of supercooling of the system, the scenario of homogeneous crystalline nucleation is realized at the initial stage of the phase transition. Keywords: molecular dynamics, crystallization, methane hydrate.