Antimicrobial peptides (AMPs) are attractive materials for combating the antimicrobial resistance crisis because they can kill target microbes by directly disrupting cell membranes. Although thousands of AMPs have been discovered, their molecular mechanisms of action are still poorly understood. One broad mechanism for membrane disruption is the formation of membrane-spanning hydrophilic pores which can be stabilized by AMPs. In this study, we use molecular dynamics simulations to investigate the thermodynamics of pore formation in model single-component lipid membranes in the presence of one of three AMPs: aurein 1.2, melittin and magainin 2. To overcome the general challenge of modeling long time scale membrane-related behaviors, including AMP binding, clustering, and pore formation, we develop a generalizable methodology for sampling AMP-induced pore formation. This approach involves the long equilibration of peptides around a pore created with a nucleation collective variable by performing coarse-grained simulations, then backmapping equilibrated AMP-membrane configurations to all-atom resolution. We then perform all-atom simulations to resolve free energy profiles for pore formation while accurately modeling the interplay of lipid-peptide-solvent interactions that dictate pore formation free energies. Using this approach, we quantify free energy barriers for pore formation without direct biases on peptides or whole lipids, allowing us to investigate mechanisms of pore formation for these 3 AMPs that are a consequence of unbiased peptide diffusion and clustering. Further analysis of simulation trajectories then relates variations in pore lining by AMPs, AMP-induced lipid disruptions, and salt bridges between AMPs to the observed pore formation free energies and corresponding mechanisms. This methodology and mechanistic analysis have the potential to generalize beyond the AMPs in this study to improve our understanding of pore formation by AMPs and related antimicrobial materials.