In simple terms, it's an easy walk and there is nothing you couldn't figure out on-site. (That's easy to say for someone who never did it with two children, one in a stroller.)

At 0630, I would expect no problems. There is a pedestrian overpass that I chose not to use because it's a bunch of steps up and down with no elevator or escalator. With luggage, I would expect you to do the same, and you would need to wait for a break in traffic.

In more detail (and this will make more sense if you are looking at a satellite view in your map program), cross the street just out the front door of the hotel. You will be walking west. This street is not busy, but stay safe. Turn right and walk around the parking structure the long way. When you get to the pedestrian bridge, wait for a break in traffic, then cross what Google Maps calls Faggs Road. Alternatively, walk to the crosswalks at Great South-West Road.

Alternatively, when you come out of the hotel, turn left and walk until you can cross the not-busy street and get to the sidewalk on the south side of the parking structure. (If you want to do this, you might be able to use a back door of the hotel.) Walk near the parking structure until you can cross Faggs Road. This looks like it should be shorter, but not by much, and it would be louder, but it does put you right at the pedestrian crossing.

If you want to be super-safe, you would take the pedestrian bridge over Faggs Road. You will probably make that call at the time, based on traffic and how daunting those stairs look.

FWIW, there is a free bus. With luggage and children, I would be reluctant to try this, even at 0630.