Haneda to Hamamatsucho station at peak hour

Hi, my flight arrives at Haneda airport at 5:55AM. I am travelling with 2 small children. I'm guessing that by the time we are ready to leave the airport it would be between 730AM-8AM. This will coincide with the peak hour. I was wondering if it would be possible to still take the monorail to Hamamatsucho as our accommodation is located there or should we just avoid the peak hour by taking a taxi as we are traveling with children. Any advice would be appreciated, thanks!

You travel against the peak hour traffic. The amount of people on board of the monorail should not be too large.