Create rows of data into table that do not have a specific column value

I have a table that has missing information that needs to be inserted with very specific conditions. However, I am unsure on how to proceed.

I have one table that contains an overall view of information. Using Projects as an example

I have another table that contains a subset of information of the first table which shows the Statuses and Timeline of those projects.

As you can see from the second table, there is no entry for when Project B 'started' and there is no entries for Project C at all.

I want to add entries for Projects missing a 'started' status with the arbitrary date: 1/1/2000. So the new second table would look like this:

The first way I thought of was to get all of the Projects that don't have the desired status, but the results of the script I created came out wrong.

SELECT t.ProjectID FROM t1 t
INNER JOIN t2 tt ON t.ProjectID = tt.ProjectID
WHERE pp.ProjectStatus != 'Started'

I then tried going the other direction and found all the Projects that do have the desired status and I succeeded in doing that.

SELECT ProjectStatusID, ProjectID, ProjectStatus FROM t2
WHERE ProjectStatus NOT IN (SELECT ProjectStaus FROM t2
WHERE ProjectStatus != 'Started')

However, I am unsure how to use this result column in another script. I could obviously do a long string using the Where clause and copying a pasting all of the ProjectID values, but that is obviously inefficient, especially if there were many more Projects than the ones I gave in the example above.

I think you just want NOT EXISTS to check which Projects are missing the 'Started' status.

insert into ProjectStatus (ProjectId, ProjectStatus, [Date])
select ProjectId, 'Started', '1/1/2000'
from Project p
where not exists (
  select 1
  from ProjectStatus ps
  where ps.ProjectId = p.ProjectId
  and ps.ProjectStatus = 'Started'
);

And if you wanted to only add the 'Started' status only to projects which had at least one status recorded, but don't have a 'Started' status (which isn't what you asked) then you could just check for the missing ProjectStatus using GROUP BY and HAVING e.g.

select ProjectId, 'Started', '1/1/2000'
from ProjectStatus
group by ProjectId
having sum(case when ProjectStatus = 'Started' then 1 else 0 end) = 0;

DBFiddle