Generative recommendation (GR) has demonstrated substantial potential for sequential recommendation in an end-to-end generation paradigm. However, existing models suffer from severe cold-start collapse, i.e., recommendation accuracy on cold-start items drops to near zero. Current solutions rely on retraining with cold-start interactions, which faces sparse feedback, high computational cost, and delayed updates, diminishing practical utility in rapidly evolving catalogs in recommendation. Inspired by NLP model editing (enabling training-free knowledge injection into large language models), we explore applying this paradigm to generative recommendation, but face two fundamental challenges: (1)~sequential data in GR lacks explicit subject–object binding (a core NLP sentence structure), hindering targeted model edits; (2)~sequential data in GR has no fixed token co-occurrence patterns (unlike NLP's stable phrases), making multi-token injection unreliable. To address these, we propose GenRecEdit, the first model editing framework tailored for generative recommendation. Specifically, we: (1)~mitigate the absence of sentence structure by explicitly modeling the intrinsic relationship between the entire sequence context and the next-token (e.g., semantic IDs, SIDs) generation; (2)~adopt iterative token-level edits to effectively inject token bundles (e.g., items); and (3)~introduce a One-One trigger mechanism to avoid interactions among multiple token-level edits during inference. Extensive experiments across multiple datasets demonstrate that øurname substantially improves recommendation performance on cold-start items while preserving the model's original recommendation quality. Moreover, øurname achieves these gains with only approximately 9.5% of the training time required by retraining, significantly reducing computational cost and enabling efficient, frequent model updates.