Clonal dynamics within hematopoietic stem cells (HSCs) provide critical insights into both hematopoietic regeneration and the development of hematological diseases. Advances in sequencing technologies and temporal clonal analysis have revealed that mutations driving clonal dominance often emerge early in life and gradually expand over decades. This slow progression, often coupled with sub-percentage clonal abundances, presents significant challenges in detecting and monitoring clones that may contribute to disease development. Using a stochastic mathematical model of clonal competition at HSC level, we take a novel approach to investigate the limitations of accurately quantifying the dynamics of small but slowly expanding clones over short observation periods. Our results provide new insights showing that intrinsic stochastic fluctuations dominate early-stage clonal competition, particularly for low-abundance clones (around 1% clonal contribution), leading to an overrepresentation of apparently stable or shrinking clones in short-term analyses. Measurement uncertainty and limited sampling intervals further complicate accurate inference of clonal growth. Furthermore, we investigate the impact of increased proliferative activity, potentially driven by chronic inflammation, on clonal progression. Our model shows that higher proliferation rates act as a time-lapse mechanism accelerating the expansion of pre-malignant clones. Our findings underscore the challenges of short-term monitoring in identifying and tracking slowly expanding clones. They also highlight the need for extended follow-up periods and improved measurement precision to accurately assess clonal dynamics in clinical and therapeutic contexts. While simplified, our approach offers valuable insights into clonal competition and serves as a cautionary reminder about the limitations of inferring clonal behavior from short-term data.