Aircraft landing gear shock absorber simulation is challenging due to the rich multiphysics nature of the internal dynamics and the scarcity of publicly available data from experimental measurements or high-fidelity numerical simulations. In order to tackle this challenge, an automated multi-fidelity and multiphysics capable framework has been developed to facilitate the efficient simulation of oleo-pneumatic shock absorbers, whether at a system level using low-fidelity two-equation dynamic system models, or diving deeper into the internal dynamics using steady and unsteady simulations that provide a more detailed understanding of the internal flow regimes under different shock absorber layouts and loading profiles. The present work focuses on expanding this capability to cover shock absorber design exploration, with the aim of reaching an efficient process of algorithm training and design optimization. To that end, a preliminary data-intensive Artificial Neural Network (ANN) training and design optimization exercise were conducted using the low-fidelity dynamic system model solver. The use of efficient Design of Experiment (DoE) sampling techniques becomes increasingly important on moving to higher fidelity simulations, where the high computational cost provides a strong motivation to limit the number of high-fidelity simulation samples to the minimum possible required for the development of surrogate models, which can then be used to populate the design space and conduct optimization studies. The low-fidelity preliminary study provides a baseline to compare against as more efficient design of experiment sampling techniques are implemented. These are initially applied to the low-fidelity model to compare the prediction of surrogate models developed using different sampling methods against the baseline, where the improvement in efficiency associated with each approach can be quantified. Finally, the surrogate models developed from different fidelity-levels can be compared utilizing an assessment of the level of uncertainty and the performance variation predicted by the inclusion of that fidelity level. This enables a cost against benefit evaluation of the various routes using fidelity-level and sampling method combinations for surrogate model development. The overall framework provides a holistic solution for driving progress in design, while reducing the risk of working on challenging simulation problems in the absence of external data for validation.