Long ago the Internet could not be accessed ….
I am looking for a word to use in the above sentence. I want it to mean ‘easily’ and ‘quickly’. I remember there was a phrase or proverb which had the word ‘finger’ in it.
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Long ago the Internet was not at everybody’s fingertips.
It’s slightly awkward in this example sentence — it works better when the active agent is more explicit (e.g. “When I was a kid, we didn’t have the internet at our fingertips.”) But otherwise it seems to fit exactly what you have in mind: it means something is easily and quickly accessible at any time, and involves fingers.
(Also suggested by Esther in comments on the question.)
There is a possibility of using a fixed expression that has "fingers" in it, but it would probably be better to use it in the present case as introduced by another fixed expression ("just like that").
(ref.) … turned back over his shoulder but not toward me, stared for what seemed like a whole lot longer than a couple seconds as if he'd tranced out just like that, at the snap of the fingers, as if he was staring suddenly at something in