3D object detection models that exploit both LiDAR and camera sensor features are top performers in large-scale autonomous driving benchmarks. A transformer is a popular network architecture used for this task, in which so-called object queries act as candidate objects. Initializing these object queries based on current sensor inputs is a common practice. For this, existing methods strongly rely on LiDAR data however, and do not fully exploit image features. Besides, they introduce significant latency. To overcome these limitations we propose EfficientQ3M, an efficient, modular, and multimodal solution for object query initialization for transformer-based 3D object detection models. The proposed initialization method is combined with a "modality-balanced" transformer decoder where the queries can access all sensor modalities throughout the decoder. In experiments, we outperform the state of the art in transformer-based LiDAR object detection on the competitive nuScenes benchmark and showcase the benefits of input-dependent multimodal query initialization, while being more efficient than the available alternatives for LiDAR-camera initialization. The proposed method can be applied with any combination of sensor modalities as input, demonstrating its modularity.