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In order to initiate streamers and leaders under thunderstorm conditions the electric field should reach values higher than the critical breakdown field Ek (i.e., similar to 30 kV/cm/atm. However, the maximum electric field in thunderstorms measured by balloons is similar to 6-9 kV/cm/atm. In present work, to achieve the electric field amplification required for streamer initiation, a system of two approaching spherical hydrometeors is investigated. Streamer initiation is determined from a Meek number, describing electron multiplication in fields above Ek. We have found the relationships between radii of particles for successful streamer initiation in the gap between these two particles and also on the outside periphery of the two-particle system when the particles are connected by a discharge channel. Furthermore, we estimated the frequency of streamer initiation using three realistic hydrometeor size model distributions available in the literature and found that the scenario of streamer initiation on the outside periphery is only possible for relatively high electric fields >= 0.5Ek at altitudes of 3 and 6 km.