A quick web search shows most sources stating that cats begin to purr from the age of 2 days but it's often not loud enough to be easily noticed by the human ear.
My cat has only started purring recently. He is four years old. And even then it is only a very light rumble occasioally. He is the only cat I have had that doesnt really purr,
I have 2 cats and one purrs constantly and very loudly. The other seems to purr a lot less but his purring is all breath and no voice - kind of a whispered purr so not nearly as noticeable. Your kitten possibly is purring but just too quiet for you to hear.
They all purr, but many purr at different things - your kitten is very new to you, probably still feels a bit uncertain. She'll purr once she settles in.
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