Given his symptoms I would have him tested, just to rule things out

Sounds a lot like my son in preschool. We eventually sought professional advice and after they assessed him he was found to be gifted but also has a sensory seeking sensory processing disorder. Sometimes seeking SPD is misdiagnosed as ADHD the difference is usually distinguishable by whether they are struggling academically or are still doing well. My son is doing OK now in second term of kindergarten. 4 is young for a boy in kindergarten. They recommended my son wait till he was 5 before starting despite being gifted because boys are more inclined to struggle with behaviour when they are younger. They say it can take a whole term for kids to adjust to school especially if they are not used to formal education settings prior to starting. If you are concerned then you could have him assessed but regardless of diagnosis try behavioural therapies before medication.