Abstract: Synthesizing believable 4D hand-object grasping sequences is important for character animation, extended reality, and embodied agents. Grasping requires a hand to approach, contact, and lift or manipulate an object coherently. Existing synthesis methods often model only the final static grasp or rely on additional conditions, such as language, target grasps, or object trajectories, to specify the interaction. We instead study the underconstrained problem of generating a complete grasping motion from a single initial hand-object state. Our framework decouples hand-motion generation from object-motion recovery. Given an object point cloud in the initial wrist frame and the initial parameterized hand configuration, conditional flow matching predicts a sequence-level contact map and a hand pose at each normalized sequence time. This time-indexed formulation avoids the error accumulation of autoregressive rollout while representing the complete motion. We then infer an attachment frame and recover rigid-object motion through training-free, contact-guided weighted registration. We evaluate on held-out DexYCB objects and unseen object geometries reconstructed from in-the-wild videos by Open-CHOIR. Compared with LatentHOI, our method produces smoother hand and object motion in every setting, matches or improves on its contact and penetration metrics in the wild under a shared initialization, and is about 30x faster per generated frame. In a 15-participant study, our motions were preferred in roughly two thirds of (forced-choice pairwise) comparisons. Precise contact closure on novel geometry, however, remains a key open challenge.