Step 1 of 4: Condition for a fluid at rest
Intuition
Every tiny 'droplet' of water in the vessel sits still because surrounding forces cancel it perfectly — if any net force remained, it would have started flowing.
Analysis
A fluid at rest in a closed vessel means every infinitesimal fluid element is at rest: by Newton's second law, the net force on each element is zero. This is the sole starting point of hydrostatics — every conclusion about pressure follows from this balance condition.