In engineering design for multi-stage HF treatments of horizontal well stimulation, it is ideal to promote simultaneous growth of all fractures in each stage in order to reduce the number of non-producing perforation clusters. While increased attention has been given to studies of multiple HF growth, time dependence is not typically considered as a factor affecting the HF initiation and following growth. A combined experimental and modeling study is carried out to explore the occurrence of the time-dependent initiation of single/multiple hydraulic fracture(s) and their subsequent propagation. By showing the existence of HF initiation at wellbore pressures that are insufficient to induce instantaneous initiation, and explaining that its underlying mechanism is due to the stable growth of the hydraulic fracture under subcritical conditions, this research leads to new insights for promoting more evenly growth of multiple hydraulic fractures in multi-stage HF treatments. Furthermore, our experimental results indicate that the time delay associated with hydraulic fracture initiation can be affected by various factors, such as the fluid viscosity and acidity, and the confining stresses, thereby leading to the practically-relevant outcome that fluid(s) can be chosen in order to promote initiation and growth of multiple hydraulic fractures and/or single hydraulic fractures under conditions where the required wellbore pressure for instantaneous initiation cannot be reached.