The InterGalactic Magnetic Field (IGMF), which could permeate the cosmic voids but was never detected so far, is considered a relic of the early Universe. Constraints on its strength $B$ can be derived from its influence on time-delayed very-high-energy photons from Gamma-Ray Bursts (GRBs) in the electromagnetic cascades along their path to the Earth. The present lower limit achieved on its intensity is $10^{-18}\;\mathrm{G}$. In this work, we simulate data from the Cherenkov Telescope Array Observatory (CTAO), accounting for realistic observational constraints, and we apply a joint spectral and temporal fit to characterize the IGMF. GRBs 190114C and 221009A are used as test cases to assess the sensitivity of CTAO. They demonstrate that a broad range of IGMF strengths can be probed with a lower bound as high as $10^{-15}\;\mathrm{G}$. Notably, we show that observations by the CTAO first large telescope, LST-1, already allow us to exclude field strengths up to $3\times 10^{-17}\;\mathrm{G}$.