Pristine metal–organic frameworks (MOFs) generally suffer from low mechanical strength and poor processability, hindering their direct application in fixed-bed adsorption systems. In this work, we propose a stepwise impregnation strategy that enables uniform in-situ crystallization of UTSA-16(Co) within amino-functionalized polyacrylate (PAA-NH₂) matrices via pre-anchored cobalt ion sites, designed to overcome the low loading and inhomogeneous distribution issues of conventional one-step impregnation methods. Three synthesis protocols (one-step impregnation, stepwise impregnation, and secondary growth) were systematically compared, and the stepwise approach achieved the highest MOF loading of 53 wt%. The optimal composite exhibited a thermogravimetric (TGA) pure-CO₂ uptake of 95.0 mg/g at 25 °C and 1 bar and retained 98.6% of its initial capacity after 10 consecutive adsorption–desorption cycles, indicating good short-term cyclic stability. Systematic fixed-bed tests revealed that the empirical Avrami fractional-order model (R² ≥ 0.994) accurately described the heterogeneous adsorption kinetics of the composite, and the dynamic breakthrough behavior was jointly regulated by gas flow rate, bed temperature, inlet CO₂ concentration, and relative humidity. The composite was found to be moisture-sensitive: at 60% RH, the capacity fell by 52.6%. A desorption efficiency above 99% was achieved within 20 min under optimal conditions (90 °C, 0.6 L/min purge gas). Overall, this work provides systematic kinetic data and operational guidelines for the optimization of MOF–polymer composite adsorbents in laboratory-scale fixed-bed applications.