Generally, if you apply before the end of the month of July, you are considered an early applicant. Applications submitted during the first month month are immediately processed but not sent to dental schools until the last Friday of June as a single giant batch. Then applications are reviewed by dental schools and may start sending interview invites shortly after while other schools may wait until late September or early October (it varies for each dental school). As a result, submitting on the first day does not have a significant advantage over submitting at the end of June. Ultimately, you should submit as soon as you have everything ready. Every day can potentially help you get into your dream school!
There isn’t a distinct cut-off for what is defined as an early applicant. Think of it as a gradient throughout the cycle. The later it is in the cycle one submits, the less early an applicant is.