Sulfur or peroxide crosslinking is the most common and conventional method to develop elastomeric materials. A new approach to crosslink epoxidized natural rubber (ENR) by aminopropyl terminated polydimethylsiloxane (AT-PDMS) is described, intending to develop a new kind of hybrid organic–inorganic elastomers. The curing reaction is accelerated by using hydroquinone as a catalyst. The formation of the hybrid structure is evident from the appearance of two glass transition temperatures, at −1 and −120 °C, for the ENR and PDMS phases, respectively. The curing reaction is found to be of first order with respect to amine concentration with the estimated activation energy of ≈62 kJ mol⁻¹. Comparing the mechanical properties to a typical ENR-sulfur system leads to the conclusion that the ENR/AT-PDMS hybrid structure is highly stretchable and soft, as demonstrated by its relatively higher strain at failure (up to ≈630%), and lower hardness and modulus values. The higher stretchability and soft nature of the material are achieved by introducing flexible PDMS chains during the curing process resulting to a hybrid elastomer networks. This kind of soft but robust materials can find several applications in diverse fields, such as soft robotics, flexible, and stretchable electronics.