A novel method for accurately identifying the large strain elastic response of elastomeric materials is presented. The method combines the data-driven identification (DDI) algorithm with a unique heterogeneous experiment, deviating from the conventional approach of conducting multiple simple experiments. The primary objective of the method is to decouple the experimental process from the fitting technique, relying instead on a single comprehensive experiment to generate an extensive collection of stress and strain energy fields. This collection is then used in conjunction with a standard fitting technique to determine the parameters of hyperelastic models. Notably, the approach places significant emphasis on the strain energy density field as a critical factor in model identification, as it encompasses the full material response within a single scalar quantity. To demonstrate the effectiveness of the proposed approach, a proof of concept is provided using synthetic data. The results highlight the efficiency of the method and emphasize the importance of incorporating the strain energy density field for precise model identification, surpassing the reliance on stress data alone. In addition, several graphical tools are introduced to evaluate and analyze the quality of both the generated mechanical fields and the identification results. The proposed approach offers a more comprehensive representation of the material behavior and enhances the reliability and prediction capabilities of hyperelastic material models. It holds significant potential for advancing the field of solid mechanics, particularly in accurately characterizing the mechanical responses of elastomeric materials.