EEA2: COA + Work + National Insurance Card

Hi,

Timelines of my Applications:
EEA2 Application sent by Mail on August 19, Received the COA on Sept 2.
the letter confirms I am permitted to work. Does that mean I can apply for a NI in the Job Center now and possibly find a job? Will that affect my application if I applied for a Job seeker's allowance whilst waiting for a job?

*Or it is not possible unless I have my passport with me.

Thanks!

Job center staff will not process NINO unless seeing your passport. You can try your national identity card, they may accept it (before doing that ask them in advance).