In the sprite halo events produced by cloud-to-ground lightning discharges, the spatial offsets, long delays, and polarity asymmetry related to the inception of sprite streamers are yet to be explained consistently with observations. In the present work, we use a two-dimensional model and a high-resolution one-dimensional plasma fluid model accounting for electron impact ionization, dissociative attachment, and photoionization processes to simulate halo events. In order to monitor the inception of sprite streamers, that cannot be modeled with present computer resources in the framework of fluid models, we use an improved avalanche-to-streamer transition criterion and investigate the response of the lower ionosphere to the charge moment changes induced by lightning discharges as a system of avalanches. On the basis of simulation results, we suggest a new mechanism for the inception of sprite streamers, explaining specifically how they can be triggered spatially outside of and temporally separated from the main sprite halo. The inception of sprite streamers is demonstrated to depend strongly on the charge moment change and the ambient electron density profile, which together determine the size of the streamer initiation region. We show that sprite streamers are mostly triggered by positive cloud-to-ground lightning discharges mainly because of mechanisms related to direction of propagation of electron avalanches. Moreover, the triggering of long-delayed sprites is demonstrated to be a unique property of halos produced by positive cloud-to-ground lightning discharges due to the formation of a long-lasting high-field region. Lightning continuing current can enlarge this high-field region and pull it down to lower altitudes where electron density is lower, extending the streamer initiation region.