Many testing and benchmarking scenarios in software and systems engineering depend on the systematic generation of graph models. For instance, tool qualification necessitated by safety standards would require a large set of consistent (well-formed or malformed) instance models specific to a domain. However, automatically generating consistent graph models which comply with a metamodel and satisfy all well-formedness constraints of industrial domains is a significant challenge. Existing solutions which map graph models into first-order logic specification to use back-end logic solvers (like Alloy or Z3) have severe scalability issues. In the paper, we propose a graph solver framework for the automated generation of consistent domain-specific instance models which operates directly over graphs by combining advanced techniques such as refinement of partial models, shape analysis, incremental graph query evaluation, and rule-based design space exploration to provide a more efficient guidance. Our initial performance evaluation carried out in four domains demonstrates that our approach is able to generate models which are 1-2 orders of magnitude larger (with 500 to 6000 objects!) compared to mapping-based approaches natively using Alloy.