This paper indicates that it is possible that children can show giftedness shortly after birth by:
alertness, response to caretakers, advanced motor control, early development of intentionality or
unusual attention span
In that same paper is a summary of a study where parents of gifted children were asked to retroactively identify early signs of giftedness.
The most frequent signs
of giftedness found in this study included long attention span, excellent memory, early and
extensive vocabulary development, curiosity, early reading ability, rapidity of learning, and the
ability to generalize concepts. Other studies have revealed additional characteristics:
imaginary companions, high activity levels, less need for sleep, ambidexterity, unusual
responsiveness to caretakers, allergies, sense of humor, sensitivity, perfectionism, concern with
morality and justice, preference for older playmates, and fascination with books.
The most interesting thing about the paper is the "maybe, but maybe not" aspect of most of the signs listed. Maybe your extremely verbal infant is gifted, but maybe your silent infant is like Einstein and will start speaking in complete sentances at age 4. Maybe your early walker is gifted, but maybe he or she is simply one of the non-gifted early walkers.
Here is another summary of a study on gifted children that retroactively looked at the signs of giftedness they displayed as infants and toddlers:
94% were very alert as infants.
94% had a long attention span as an infant or toddler.
91% showed early language development.
60% showed early motor skill development.
48.9% were ambidextrous at some period of their development.
37% had imaginary playmates.
The mean age at which these children spoke their first word was 9 months.
The mean age at which the children sight-read an easy reader was before 4. (Rogers & Silverman, 1997)
This site has a long list of the signs of a young gifted child, although many are applicable to the toddler and preschool stages rather than the infant stage.
The specific 10 month old described has some signs of giftedness, and it certainly would not hurt to expose him to as many challenges as he is interested in. However it appears that the signs of giftedness expressed in infancy are at best inconclusive guides, and signs in the toddler and preschool years are more definitive. Even if any given infant does not meet some external criteria for "gifted," that child should be given a chance to learn and grow to the best of his or her abilities.