I just filled in as "guest instructor" at one of our QuickStart after school programs in Pelham, N.Y. for kindergartners, about 5-years-old. There were 12 children in the class. Each child had a racquet and sponge ball.
The first exercise was hitting the ball up with the racquet, letting the ball hit the ground, and then hitting it up with the racquet again. NOBODY COULD DO IT(actually one kid could, but 11 couldn't)! I had the kids put their racquets away. We started a progression with sponge balls only.
The first exercise was to bounce the ball on the ground and catch it in their hands. Once they could do it 10 times in a row, the next exercise was throw it up and catch it. Then throw it up, clap once and catch it. Then clap twice, three times, etc. Another exercise was walking across the gym and bouncing the ball. After that, throwing the ball against the wall & catching it.
It's very important to start at the 'beginning', not in the 'middle' of a progression. In this case, the beginning was without racquets.
At the end of the class, we played a game with racquets. Some of the kids were able to meet the ball and it was a successful game.
For young children under the age of six, start with hand-eye exercises, throwing a ball and catching it, even rolling it and trapping it. Once an exercise is mastered, move to the next progression. Don't skip any, it can be discouraging to the child and counter-productive.
Take your time and your child will love it!