I assume you do not want to use the plan defaults at entity level.
If you are not using these defaults and you want the dates to default to the project start and finish, there is a setting you can mark at project level:
Set Planned Cost Dates (this is a checkbox)
If you enable it, it will default to project dates.
Then you mention, you want the dates read-only. Here what you can do:
Go to Admin > Studio > Cost Plan object > Views
On the Cost Plan Properties view, go to fields
Make the Start Period and the Finish Period fields as enter once.
They will be editable in creation, defaulting to the project dates and after saving will be read-only. They will be editable only at creation.
The read-only flag is not enabled at these attributes, so the above is the only way forward I can think of.