If the teacher can't accommodate your child's needs and individual nature, look for another teacher. Find a teacher in your area. Although having an acoustica piano is not mandatory for the beginning student, it certainly is beneficial to have for the child to experiment with and create. Some companies will rent pianos. Others offer financing options for the purchase of a new or used piano.
Some people choose to get an electric keyboard initially.
If you are considering this, the keys need to be the size of normal standard acoustical piano and touch sensitive. Your child's practice space needs to have adequate lighting, ventilation, and a solid secure seat. If you have an acoustical piano, make sure that it is in tune. Remember that much of the life of a child is devoted to the exploration of new things and concepts. The more you can make the home situation like the studio, the more the child will be able to indulge his exploration instinct at home.