Try to narrow this down further, do you use restrictions at all? I don't think that there is anything in the restrictions setting that would disable Switch Control, but I don't use restrictions. From my limited experince with the restrictions settings, the only thing that I can think of that might be making the setting greyed out would be Settings>General>Restrictions>Allow Changes>Accounts. But I really don't think that has anything to do with this.
SInce this is a brand new iPad, try basics. Reset the iPad first. If that doesn't work, reset all settings, you will not lose any data in eituer case, but if you reset all settings, you will have to re-enter all device settings again. Resetting all settings will also restart the iPad so don't be alarmed when that happens.
First, try resetting the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
If that didn't work, try this. Reset all settings. Settings>General>Reset>Reset all Settings.