During ripening, ‘Hass’ avocado skin changes from green to purple/black. Low-temperature storage with a controlled atmosphere (CA) is the most widely used method for avocado storage; however, few studies have simulated this technology and considered the days of regular air (RA) storage prior to CA storage. Herein, the effect of delaying the storage of ‘Hass’ avocado (>30% dry matter) in a CA was examined. Long-term storage conditions (5 °C for 50 days) corresponded to (i) regular air storage (RA), (ii) CA (4 kPa O2 and 6 kPa CO2) and (iii) 10 days in RA + 40 days in a CA and (iv) 20 days in RA + 30 days in a CA. Evaluations were performed during storage and at the ready-to-eat (RTE) stage. Skin color remained unchanged during storage, but at the RTE stage, more color development was observed for fruits stored under CA conditions, as these fruits were purple/black (>50%). At the RTE stage, the anthocyanin content increased, and compared to fruit under RA, fruit under a CA contained a five-fold greater content. A 20-day delay between harvest and CA storage increased the fruit softening rate and skin color development after cold storage, reducing the effectiveness of CA as a postharvest technology for extending storage life.