I don't think there's a direct way to only allow submissions after a certain date, but I can think of 2 options that could help:
- Keep the assignment as "No submission" until the Thursday class, when you change it to the appropriate submission type
- Make it into a quiz that is password protected (so they can see the instructions, but not open the quiz until you share the password, which you do on the Thursday class).
Add a single question to that quiz, which can be a "file upload" or "essay" question, as appropriate
The main advantage of option 1 is that it can work for any assignment type, including "external tools".
Another is that if the assignment is "file upload", you can download all submissions (which you can't for a quiz, as far as I recall).
Its disadvantage is that you'd need to remember to change the submission type (not only on Thursday, but also later when you copy the class across different terms/semesters).