Some of what you will now read is quite a lot different than what a large majority of piano teachers might tell you. In fact, it may be radically different.
Let us start with a very frequent question: When should you start a child on piano lessons/. The general advice is perhaps to start them around 2nd grade or so. Any younger and it is much too difficult, as the child does not have the motor skills to master the piano.
However, I do agree that there should probably be a younger age limit if we are talking about ACOUSTIC pianos. However, with digital keyboards widely available that do not require the same set of motor skills, a child's interaction with an actual keyboard interest can start very, very young. I do not mean the digital pianos that require the same level of motor skills as does an acoustic piano. I mean a keyboard that has velocity-sensitive keys without having weighted keys. The louder you play the key the louder it will sound. But this type of digital instrument is quite easy to play.
With a child's piano lessons, there should be much more going on than learning to practice reading notes and depressing them on an acoustic piano. There is ear-training, composition and improvisation, instruction in melody, harmony, and rhythm, exposure to all types of music, and all none of these things requires an acoustic piano at all, and consequently do not require a set of more advanced motor skills.
The common argument against digital pianos and especially digital keyboards is that they can never replace an acoustic piano, and that you can learn many bad habits on a digital keyboards, especially one without weighted keys. However, in today's world of music, the acoustic piano is only one small subset of the people who use all sorts of keyboard instruments, many electronic.
In my humble opinion, the exposure to music is what is important, and this can start successfully much earlier in a child's life with a digital keyboard than with a piano. There are, of course, exceptionally gifted children that can and do have the motor skills to play an acoustic piano at the age of 3, but most children are just not at that point yet.
Perhaps, if your goal is to turn your child into the next Mozart, you should start him or her on the acoustic piano as soon as possible. If your goal is to enrich your child's life with music as early as possible to give her or him a life time of enjoyment, then a digital keyboard will do much better, since it is much easier in terms of motor skills, AND it can be connected to a computer.