The imbibition of hydrate dissociation water into the sediment can lead to fracture expansion and complete dispersion of the skeleton structure, which impacts the depressurization drainage of the hydrate. However, there are no studies on the initiation time of imbibition tensile cracks. In this paper, the drip imbibition method and nuclear magnetic resonance (NMR) technology are used to study the fracture initiation time of hydrate sediments and analyze the related influencing factors. The experimental results show that after water imbibition into the sediment, it will go through four stages of wetting, microfracture, fracture network, and skeleton dispersion, resulting in a two-segment curve of the fracture, and these four stages are divided according to the state of the sample, such as the number of cracks in the sample and whether the skeleton is dispersed. The rate of development of cracks will increase rapidly after reaching the critical time, which can be considered by observing the cracks on the samples. The critical time is when the state of the sample is about to change significantly, which is affected by internal and external factors. For instance, as the whole rock's initial water and mineral content increases, the critical time shortens. However, as porosity and permeability increase, or stress is added to the boundary, the critical time increases. Different fluids have different effects on the critical time; for example, oil makes the critical time be prolonged, whereas potassium chloride solution shortens the critical time. Hence, study of factors affecting the critical time is of great significance for production optimization from hydrate sediments.