Trajectory prediction of agents is crucial for the safety of autonomous vehicles, whereas previous approaches usually rely on sufficiently long-observed trajectory to predict the future trajectory of the agents. However, in real-world scenarios, it is not realistic to collect adequate observed locations for moving agents, leading to the collapse of most prediction models. For instance, when a moving car suddenly appears and is very close to an autonomous vehicle because of the obstruction, it is quite necessary for the autonomous vehicle to quickly and accurately predict the future trajectories of the car with limited observed trajectory locations. In light of this, we focus on investigating the task of instantaneous trajectory prediction, i.e., two observed locations are available during inference. To this end, we propose a general and plug-and-play instantaneous trajectory prediction approach, called ITPNet. Specifically, we propose a backward forecasting mechanism to reversely predict the latent feature representations of unobserved historical trajectories of the agent based on its two observed locations and then leverage them as complementary information for future trajectory prediction. Meanwhile, due to the inevitable existence of noise and redundancy in the predicted latent feature representations, we further devise a Noise Redundancy Reduction Former, aiming at to filter out noise and redundancy from unobserved trajectories and integrate the filtered features and observed features into a compact query for future trajectory predictions. In essence, ITPNet can be naturally compatible with existing trajectory prediction models, enabling them to gracefully handle the case of instantaneous trajectory prediction. Extensive experiments on the Argoverse and nuScenes datasets demonstrate ITPNet outperforms the baselines, and its efficacy with different trajectory prediction models.