Modeling 3D scenes by volumetric feature grids is one of the promising directions of neural approximations to improve Neural Radiance Fields (NeRF). Instant-NGP (INGP) introduced multi-resolution hash encoding from a lookup table of trainable feature grids which enabled learning high-quality neural graphics primitives in a matter of seconds. However, this improvement came at the cost of higher storage size. In this paper, we address this challenge by introducing instant learning of compression-aware NeRF features (CAwa-NeRF), that allows exporting the zip compressed feature grids at the end of the model training with a negligible extra time overhead without changing neither the storage architecture nor the parameters used in the original INGP paper. Nonetheless, the proposed method is not limited to INGP but could also be adapted to any model. By means of extensive simulations, our proposed instant learning pipeline can achieve impressive results on different kinds of static scenes such as single object masked background scenes and real-life scenes captured in our studio. In particular, for single object masked background scenes CAwa-NeRF compresses the feature grids down to 6% (1.2 MB) of the original size without any loss in the PSNR (33 dB) or down to 2.4% (0.53 MB) with a slight virtual loss (32.31 dB).