All users (except collaborators) on all account types can create backlogged tasks.
Backlogged tasks are tasks that don't have scheduled start and end dates.
New tasks are created as backlogged by default and remain that way unless you add start and end dates to the task or convert it to a milestone.
Backlogged tasks aren't visible on the timeline portion of Gantt Chart (because they don't have scheduled start and end dates).
Open the task you'd like to convert to backlogged.
Click the date section on the left of the task.
Click Clear dates at the bottom of the date picker.
Yes, it's possible to do that from the date picker in Task view or Table view.
Yes, you can change the default option in Settings. Click on your profile picture in the upper-right corner of your workspace, select Settings, and scroll to Tasks & Subtasks. Here you can select the default start date and duration for tasks.