This study investigates the expected cosmic‐ray exposure (CRE) of meteorites if they were to be ejected by a near‐Earth object, that is, from an object already transferred to an Earth‐crossing orbit by an orbital resonance. Specifically, we examine the CRE ages of CI and CM carbonaceous chondrites (CCs), which have some of the shortest measured CRE ages of any meteorite type. A steady‐state near‐Earth carbonaceous meteoroid probability density function is estimated based on the low‐albedo near‐Earth asteroid population, including parameters such as the near‐Earth dynamic lifetime, the impact probability with the Earth, and the orbital parameters. This model was then compared to the orbits and CRE ages of the five CC falls with precisely measured orbits: Tagish Lake, Maribo, Sutter's Mill, Flensburg, and Winchcombe. The study examined two meteoroid ejection scenarios for CI/CM meteoroids: Main Belt collisions and ejections in near‐Earth space. The results indicated that applying a maximum physical lifetime in near‐Earth space of 2–10 Myr to meteoroids and eliminating events evolving onto orbits entirely detached from the Main Belt (Q < 1.78 au) significantly improved the agreement with the observed orbits of carbonaceous falls. Additionally, the CRE ages of three of the five carbonaceous falls have measured CRE ages one to three orders of magnitude shorter than expected for an object originating from the Main Belt with the corresponding semi‐major axis value. This discrepancy between the expected CRE ages from the model and the measured ages of three of the carbonaceous falls indicates that some CI/CM meteoroids are being ejected in near‐Earth space. This study proposes a nuanced hypothesis involving meteoroid impacts and tidal disruptions as significant contributors to the ejection and subsequent CRE age accumulation of CI/CM chondrites in near‐Earth space.