Contemporary artificial intelligence systems primarily rely on reward optimization, supervised objectives, or task-specific fine-tuning. While effective in narrow domains, such approaches struggle to produce persistent identity, coherent reasoning across contexts, and robust generalization. We introduce Latent Cognitive Elicitation (LCE), a novel paradigm that reframes intelligence formation as a process of eliciting internal coherence from large latent models rather than explicitly training behaviors. LCE proposes enforcing internal consistency, identity persistence, and causal stability across counterfactual environments as the primary drivers of intelligence emergence. We present formal mathematical objectives, define five novel cognitive pressure fields, introduce new evaluation metrics (Cross-Context Coherence Score, Identity Persistence Index, Counterfactual Stability Measure, Emergent Reasoning Score), derive theoretical bounds on coherence dynamics, and outline an experimental methodology suitable for supercomputer-scale validation. LCE represents a fundamental shift from optimizing task performance to stabilizing cognitive configurations, offering a new research direction toward more general, robust, and cognitively grounded AI systems.