For each child who is six years old and younger, one adult may accompany that child for Family Boarding, which takes place between the "A" and "B" boarding groups.
There may be a sizable number booked on the flight who hold either A-List Preferred or A-List status. Those customers are automatically assigned boarding numbers starting with A16, which means higher boarding numbers for all others on the flight - even those who purchased Early Bird.
You can check to see if the flight is full by trying to search for available seats on your flight, starting with looking for eight seats; if eight seats are not available, lower the number. If one seat is not available, your flight's probably full. If so, keep in mind that even in the higher "B" boarding numbers, there likely will be quite a few open seats, unless there are many thru passengers who boarded at a previous stop.
You most likely will not have a problem finding three seats together.