Change is hardly a new feature in human affairs. Yet something has begun to change in change. In the face of a range of emerging, complex, and interconnected global challenges, society’s collective governance efforts may need to be put on a different footing. Many of these challenges derive from emerging technological developments – take Artificial Intelligence (AI), the focus of much contemporary governance scholarship and efforts. AI governance strategies have predominantly oriented themselves towards clear, discrete clusters of pre-defined problems. We argue that such ‘problem-solving’ approaches may be necessary, but are also insufficient in the face of many of the ‘wicked problems’ created or driven by AI. Accordingly, we propose in this paper a complementary framework for grounding long-term governance strategies for complex emerging issues such as AI into a ‘problem-finding’ orientation. We first provide a rationale by sketching the range of policy problems created by AI, and providing five reasons why problem-solving governance approaches to these challenges fail or fall short. We conversely argue that that creative, ‘problem-finding’ research into these governance challenges is not only warranted scientifically, but will also be critical in the formulation of governance strategies that are effective, meaningful, and resilient over the long-term. We accordingly illustrate the relation between and the complementarity of problem-solving and problem-finding research, by articulating a framework that distinguishes between four distinct ‘levels’ of governance: problem-solving research generally approaches AI (governance) issues from a perspective of (Level 0) ‘business-as-usual’ or as (Level 1) ‘governance puzzle-solving’. In contrast, problem-finding approaches emphasize (Level 2) ‘governance Disruptor-Finding’; or (Level 3) ‘Charting Macrostrategic Trajectories’. We apply this theoretical framework to contemporary governance debates around AI throughout our analysis to elaborate upon and to better illustrate our framework. We conclude with reflections on nuances, implications, and shortcomings of this long-term governance framework, offering a range of observations on intra-level failure modes, between-level complementarities, within-level path dependencies, and the categorical boundary conditions of governability (‘Governance Goldilocks Zone’). We suggest that this framework can help underpin more holistic approaches for long-term strategy-making across diverse policy domains and contexts, and help cross the bridge between concrete policies on local solutions, and longer-term considerations of path-dependent societal trajectories to avert, or joint visions towards which global communities can or should be rallied.