Yes, the early arrival would be a problem, but if you're traveling with children, they may simply enjoy riding the monorail and maybe having breakfast or a snack at a coffee shop in the Hamamatsucho area.

Pronto has a good selection of pastries (some of them admittedly odd by Western standards-- but also some totally non-controversial) and beverages in the morning before converting to a pasta restaurant later in the day. There are also the old familiar Starbucks and local chains such as Doutor (limited food options) and Tully's.

Both Pronto and Doutor are located next door to each other about two blocks from the station on the street that runs west from the southern exit of Hamamatsucho Station. (In case you haven't heard, most Tokyo streets have no names.)

The monorail route runs partly along Tokyo Bay, past a horse racing track, and into the city proper, so it's an interesting view for a first-time visitor.