As salamu alaykum sister,
Bullying is a common problem and affects many children. As your child is a bully, and he is young, it is now a good time to “nip it in the bud”. While you did not state if the bullying behavior occurs only at school, please do keep a journal and notate when the bullying occurs and under what conditions. Also, you may want to see if he has ever been bullied by anyone as sometimes bullying can be a learned behavior.
Children at this age often bully when they are anxious, or if if the home environment is bossy or over-controlling (they then replicate the behavior), or if they are feeling a sense of low self esteem. In order to combat his need to bully, try to re-enforce his positive qualities, tell him you love him often, yet teach him about consequences if he does bully. As you mentioned you use time out at home for his bad behaviors at school yet that has not worked, try a different approach. For instance, if he hit his school mate for not giving him a truck, make sure you talk to him about how it must feel to be hit. Try to create a sense of empathy in you child so that he will be less prone to bully others.
Follow up the next day by having your child apologize to the child he hit and have him promise he will not hit again. Additionally, give your child an outlet to express his frustration. Perhaps a signal he can give his teacher when he is feeling upset or angry such as a word clue or if he is comfortable telling her he is upset or angry before a situation occurs.
Try a stress ball. Give your child a squeeze ball and tell him that when he feels upset or feels like hitting to squeeze the ball instead. Tell him you will be looking forward to reports from his teacher that his is not hitting others but rather squeezing the ball instead and reward him for his positive behavior. Always follow up however and ask him what made him upset and provide support and help him work through his feelings. There are many tips and creative advice for children who bully, please see reference.
Hopefully this is just a phase your son is going through but with perseverance, providing alternate means of expressing frustration as well as creating empathy for others, your son will leave the bullying behaviors and return to the compassionate, kind little boy you raised.
Hang in there, you are in our prayers, please let us know how he is doing.