It's no wonder young children are fascinated by the piano: it's a user friendly instrument that produces marvelous sounds with the easiest of efforts from hands and fingers. In the years up to age 6, the child has the greatest capacity for learning and exploration, a time that can include the piano and music and lay the groundwork for a lifetime of musical enjoyment.
An article by Tamar Satov in Today's Parent talks about the benefits of early lessons. (https://www.todaysparent.com/kids/start-music-lessons/) "In the same way that children who learn a second language at a younger age often become more fluent than those who start later, a recent study from Concordia University and the Montreal Neurological Institute suggests there are significant benefits to early music lessons. Brain scans of musicians who started training on an instrument before age seven showed stronger connections between motor regions – areas of the brain that help plan and carry out movements such as fingering and coordinating both hands – than those who began lessons later on, despite having the same amount of musical training and experience overall. Early trainers in the study also had better accuracy and precision."
Along with considering lessons, you can encourage your child's musical adventures by setting up your home with an available in-tune piano, in a 'friendly' location. Play simple games such as fingers running up and down the keyboard chasing each other; finding groups of 2 (or 3) black keys and playing all of them across the keyboard; creating a rain storm using low parts of the piano for thunder, the middle for lightning and high keys for raindrops.
Have fun singing songs using your high or low voices, or make up your own words or melodies to songs. Make rhythm instruments with common household items, and enjoy rhythm bands or playing along with your songs. Listen to a variety of music with your child and have fun attending live music performances and concerts together. Look for events like visiting a musical 'petting zoo' which in many areas is sponsored by your local orchestra and musicians.
If you have little musical experience consider taking a few lessons along with your child, and join in the fun!