We obtain a quantitative star formation history (SFH) of a shell-like structure ('shell') located in the northeastern part of the Small Magellanic Cloud (SMC). We use the Survey of the MAgellanic Stellar History to derive colour-magnitude diagrams (CMDs), reaching below the oldest main-sequence turnoff, from which we compute the SFHs with CMD-fitting techniques. We present, for the first time, a novel technique that uses red clump (RC) stars from the CMDs to assess and account for the SMC's line-of-sight depth effect present during the SFH derivation. We find that accounting for this effect recovers a more accurate SFH. We quantify an $\sim$7 kpc line-of-sight depth present in the CMDs, in good agreement with depth estimates from RC stars in the northeastern SMC. By isolating the stellar content of the northeastern shell and incorporating the line-of-sight depth into our calculations, we obtain an unprecedentedly detailed SFH. We find that the northeastern shell is primarily composed of stars younger than $\sim$500 Myr, with significant star formation enhancements around $\sim$250 and $\sim$450 Myr. These young stars are the main contributors to the shell's structure. We show synchronicity between the northeastern shell's SFH with the Large Magellanic Cloud's (LMC) northern arm, which we attribute to the interaction history of the SMC with the LMC and the Milky Way (MW) over the past $\sim$500 Myr. Our results highlight the complex interplay of ram pressure stripping and the influence of the MW's circumgalactic medium in shaping the SMC's northeastern shell.