In this study, we tackle these two barriers against the parameterization of HAIEFF force-fields using synthetic data. Firstly, we curate a database of 755 crystal structures, with corresponding optimal lattice energies and geometries derived from high-quality, solid-state DFT-D calculations for each crystal. Each entry in this database, while initially very expensive to generate, can be reused multiple times in the fitting of empirical force-fields that are consistent with different electrostatic and intramolecular energy models. The use of high-fidelity DFT-D reference data not only ensures that we are fitting to reliable data but is also congruent with the overarching CSP workflow wherein DFT-D results are usually the 'final solution' that is accepted. Secondly, we address the shortcomings in many current approaches to parameter estimation of HAIEFF models and present an efficient algorithm for multivariate optimisation of model parameters. Our approach relies on gradient-based optimisation techniques to rapidly solve large-scale parameter estimation problems. To do this, we establish a novel route for determining analytical derivatives of the parameter estimation merit function. The determination of the crystal structure for a given set of empirical parameter values is performed through our newly developed software library for performing lattice minimisation of rigid molecules known as Crystal Structure Optimizer -Rigid Molecules (CSO-RM) . CSO-RM supports calculations for either point-charge or multipole based electrostatic models, and also computes any additional analytical derivatives required by our parameter estimation algorithm. The combined implementation of CSO-RM and the parameter estimation algorithm is known as CrystalEstimator. In this paper we present our parameter estimation algorithm as implemented in CrystalEstimator and the development of the reference structure database from DFT-D calculations. The effectiveness of the implementation is evaluated on a series of test problems of increasing difficulty to demonstrate the benefits of our approach. Application of the code in the development of transferable parameter estimates will be reported in part 2 of this paper series.