One of the primary objectives of an oncology dose‐finding trial for novel therapies, such as molecular‐targeted agents and immune‐oncology therapies, is to identify an optimal dose (OD) that is tolerable and therapeutically beneficial for subjects in subsequent clinical trials. These new therapeutic agents appear more likely to induce multiple low or moderate‐grade toxicities than dose‐limiting toxicities. Besides, for efficacy, evaluating the overall response and long‐term stable disease in solid tumors and considering the difference between complete remission and partial remission in lymphoma are preferable. It is also essential to accelerate early‐stage trials to shorten the entire period of drug development. However, it is often challenging to make real‐time adaptive decisions due to late‐onset outcomes, fast accrual rates, and differences in outcome evaluation periods for efficacy and toxicity. To solve the issues, we propose a time‐to‐event generalized Bayesian optimal interval design to accelerate dose finding, accounting for efficacy and toxicity grades. The new design named “TITE‐gBOIN‐ET” design is model‐assisted and straightforward to implement in actual oncology dose‐finding trials. Simulation studies show that the TITE‐gBOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment while having comparable or higher performance in the percentage of correct OD selection and the average number of patients allocated to the ODs across various realistic settings.