In this paper, a phase-change model based on a geometric volume-of-fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with interfacial heat-transfer resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared with previous literature studies, the computational cost is reduced by three orders of magnitude. We investigated the impact of contact angle on nucleate boiling through direct numerical simulation (DNS). The results show that the contact angle primarily influences the bubble growth by altering the hydrodynamic behaviour within the microlayer, rather than the thermal effect. An increase in contact angle enhances contact line mobility, resulting in a slower bubble growth, while maintaining an approximately constant total average mass flux. Furthermore, the sensitivity of bubble dynamics to the contact angle diminishes as the angle decreases. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.