imperceptibly
In a way that changes so slowly you cannot notice.
Imperceptibly means changing or happening so gradually or subtly that you can't notice it while it's occurring. When something happens imperceptibly, it's like watching a plant grow: even though the plant is growing every moment, the changes are too small to see unless you compare today's plant to how it looked last week.
The sun moves imperceptibly across the sky. You never actually see it moving, but an hour later it's in a completely different position. A clever liar might imperceptibly shift their story each time they tell it, changing tiny details so gradually that no one catches the contradictions right away. Ice melts imperceptibly on a winter day when temperatures barely rise above freezing.
When something happens imperceptibly, your senses can't detect it in real time, even though the change is definitely occurring. This makes imperceptible changes particularly interesting: they can add up to something dramatic without anyone realizing it was happening. A friendship might fade imperceptibly over time, or someone's confidence might grow imperceptibly as they practice a new skill, until one day they realize they've completely transformed.