No, kittens are not born with the ability to process lactose. Kittens are born with the enzyme lactase, which helps them digest lactose, but the production of this enzyme decreases as they get older. Therefore, adult cats are not able to digest lactose.
As kittens, their stomach produces lots of lactase, which helps them digest their mother's milk. However, as they age, their bodies create less and less lactase. Like most mammals, they're technically lactose intolerant by adulthood.
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