Thwaites Glacier is rapidly evolving and could make large sea-level contributions in the coming centuries, making it essential to understand the drivers of the ongoing ice loss. Sediment-core analysis suggests that Thwaites Glacier was in a relatively steady state for millennia before its western pinning point ungrounded in the 1940s. Here, we include a first analysis of 1947 aerial imagery of Thwaites Ice Shelf, which shows that it was relatively undamaged, contrasting with the highly-damaged present-day. Additionally, the main outflow and shear margin were displaced ~15 km westwards compared to the present day. We use the MITgcm-WAVI coupled ocean-ice sheet model to create example quasi-steady pre-1940s configurations for Thwaites Glacier, including a most plausible pre-1940s state, finding that healing the damaged ice shelf is necessary to achieve this. Next, we trigger ice retreat and highlight key processes as the model evolves into the present-day configuration, including ice damage, pinning-point ungrounding driven by ocean melting, and ice piracy between eastern and western parts of Thwaites Glacier. By conducting reversibility experiments during the retreat, we find that multiple quasi-steady ice-sheet states are possible under the same ocean forcing, demonstrating the potential for tipping points in the Thwaites system. Either ice damage or increased ocean forcing can eliminate these quasi-steady states, prompting retreat resembling that observed today. Taken together, these results demonstrate that the sea-level contribution from Thwaites Glacier is not simply controlled by ocean warming in the Amundsen Sea, and is highly sensitive to ice-damage feedbacks, which must be incorporated into sea-level projections.