Hi Safal,
You can apply for intern permit without SSN and they will issue deficiency letter (it took 6 weeks in my case) and this (deficiency letter) is valid for 1 YEAR. If you think that you can submit the SSN within 1 year of deficiency letter, go-ahead and apply. Deficiency letter WILL NOT delay file processing (it took 4 weeks in my case). If you can't respond within 1 year of deficiency letter, they will close the file means you need to re-apply for intern permit.
I hope I have cleared your concerns.