Schedule

In most cases, the start date of execution of a task depends on the completion dates of other tasks. In order to be able to freely change the start date, the task must be "independent", which requires fulfillment of several conditions.

The task must not depend on other tasks, that is, the diagram object must not have incoming links.
The task must not have nested tasks, as for such a task the schedule is calculated by the nested diagram.
The diagram containing the task must be put directly into a folder, since only the folder has a completely free schedule, which does not depend on other tasks and is set individually.

Solution
Consequently, in this case the following should be checked:
If the diagram is not included in a folder, then you need to go to the parent diagram and change the type of the parent object to "Folder".
If the initial task has incoming links or a nested diagram, create a new object of type 'resource' before this task, name it "Start" (or somehow closer to the context), then draw a link from it to the initial object. For the created object, the start date will be available for change. By the way, shifting the start date in such a way, you can adjust the project plan so that it is completed by any specific date.
It remains to consider one more case: our task depends on other ones, but because of the circumstances the actual work began later. In such a situation, use the switch "Fix start date", it allows moving the start date to a later date in relation to the available start of the work.

Time is an important parameter of calendar calculations, so always appears when displaying dates and cannot be removed. However, I understood your need and will think about the possibility of its implementation in one of future updates.