Forging is a cornerstone manufacturing process, widely used to produce high-strength components for automotive, aerospace, and energy industries. While the process is well-studied and supported by a range of commercial simulation tools, these tools predominantly rely on finite strain Lagrangian formulations. This approach, however, introduces significant challenges: large mesh distortions require frequent re-meshing, and classical contact algorithms can be computationally demanding and difficult to implement. Additionally, the conversion of CAD geometries into simulation-ready data often requires considerable pre-processing effort, complicating workflows and limiting the potential for rapid design iteration and optimization. This work presents a Eulerian framework for forging simulations, which is based on an incompressible two-phase flow model and which uses two level set functions. The first level set function distinguishes between the billet and surrounding air, capturing the complex deformation of the workpiece. The second level set function only undergoes rigid body motions and is generated directly from the CAD geometry of the forging dies, enabling the integration of moving tooling and robust interaction between the die and billet. A key advantage of this approach is the elimination of traditional meshing bottlenecks: the framework directly processes CAD files (STEP/STL/IGES), automates mesh generation and facilitates the use of parametrized geometries for optimization loops. To ensure accuracy and stability, the method employs pressure enrichment to resolve discontinuities in the pressure gradient across material interfaces. Adaptive mesh refinement is utilized to precisely track the evolving interface, while contact is handled explicitly through a volume penalty term. The framework is fully thermo-mechanically coupled, solving the incompressible Navier-Stokes equations using a fractional step scheme to enhance computational efficiency. This approach however requires careful integration of the pressure enrichment to maintain consistency. Numerical examples are presented to demonstrate the framework’s performance. The results (final shape and deviation from the target shape, temperatures, strains and stresses) are compared against established Lagrangian-based forging simulations.