The high prevalence of diagnosed cases of severe neurological disorders, a significant proportion of which are epilepsy, contributes to a high level of mortality and disability in the population. Neurotrophic factors BDNF and GNDF are considered promising agents aimed at increasing the central nervous system’s adaptive potential for the development of the epileptiform activity. Despite the pronounced neuroprotective and anticonvulsant potential, an appropriate way to stimulate these endogenous signaling molecules with minimal risk of side effects remains an open question. Herein, we assessed the safety of gene therapy using original adeno-associated viral constructs carrying the genes of neurotrophic factors BDNF and GDNF in the early postnatal period of development of experimental animals. The intraventricular injection of AAV-Syn-BDNF-eGFP and AAV-Syn-GDNF-eGFP viral constructs into newborn mice was found to provide persistent overexpression of target genes in the hippocampus and cerebral cortex in vivo for four weeks after injection. The application of viral constructs has a multidirectional effect on the weight and body length characteristics of mice in the early postnatal period; however, it ensures the animals’ resistance to the development of seizure activity under audiogenic stimulation in the late postnatal period and preserves basic behavioral reactions, emotional status, as well as the mnestic and cognitive abilities of mice after simulated stress. Our results demonstrated the safety of using the AAV-Syn-BDNF-eGFP and AAV-Syn-GDNF-eGFP viral constructs in vivo, which indicates the expediency of further testing the constructs as therapeutic anticonvulsants.