Few-shot semantic segmentation (FSS) aims to segment novel classes in query images using only a small annotated support set. While prior research has mainly focused on improving decoders, the encoder's limited ability to extract meaningful features for unseen classes remains a key bottleneck. In this work, we introduce \textit{Take a Peek} (TaP), a simple yet effective method that enhances encoder adaptability for both FSS and cross-domain FSS \rev{by inducing a lightweight \textit{feature-space shift} conditioned on the support set}. TaP leverages Low-Rank Adaptation to fine-tune the encoder on the support set with minimal computational overhead, enabling fast adaptation to novel classes while mitigating catastrophic forgetting. Our method is model-agnostic and can be seamlessly integrated into existing FSS pipelines. Extensive experiments across multiple benchmarks--including COCO $20^i$, Pascal $5^i$, and cross-domain datasets such as DeepGlobe, ISIC, and Chest X-ray--demonstrate that TaP consistently improves segmentation performance across diverse models and shot settings. Notably, TaP delivers significant gains in complex multi-class scenarios, highlighting its practical effectiveness in realistic settings. A rank sensitivity analysis also shows that strong performance can be achieved even with low-rank adaptations, thereby ensuring computational efficiency. By addressing a critical limitation in FSS--the encoder's generalization to novel classes--TaP paves the way toward more robust, efficient, and generalizable segmentation systems. The code is available at https://github.com/pasqualedem/TakeAPeek.