The ability to dynamically switch polymer architecture offers an opportunity to tailor materials with responsive, tunable properties for applications ranging from therapeutics to advanced manufacturing. One possible "simple" architectural transition is the reversible switching between linear and cyclic topologies. In this work, we explore the polymer and solution characteristics that affect the dynamics of this conformational change. We perform single-chain molecular dynamics simulations with varying chain length, stiffness, and solvent quality, and quantify the dynamics of cyclization. In good and athermal solvents, cyclization time increased with molecular weight and stiffness, as expected. In poor solvents, we observed a non-monotonic trend with three distinct regimes as a function of molecular weight, ultimately resulting in a broad range of polymer design characteristics that cyclized over similar timescales. We rationalize these trends via changes in the chain configurations resulting from the interplay between solvent quality and chain stiffness. The polymer design and processing windows identified here open potential avenues for designing polymers with dynamic/switchable properties, enabling the efficient transformation of linear polymers into cyclic analogues through controlled cyclization processes.