There really is no requirement that a non-compete/non-disclosure be signed at the time of employment. However, the crucial question is whether this NCNDA is legal. That determination is based on whether it restricts competition or it is for the purpose of protecting your employer's trade secrets.
You should have an employment/business attorney review the contract.
Your rights are to refuse signing it and potentially be terminated assuming you are an at-will employee. If litigation ever ensued you could argue as a defense that it was signed under duress and no consideration received for signing...however, in certain circumstances, the continuation of your employment is sufficient on its own to support the non-compete. the signing also does not make it valid as the evil is in the details and it has to be carefully crafted/limited as to protecting employer trade secrets and confidential information...in this instance can be valid. However, absent actually reviewing the document is hard to give you any specific advice on whether it is reasonable or not. It has a greater chance to be upheld if it s narrowly construed to perhaps saying you cannot solicit employer customers for 1-2 years after you terminate (technically a non-solicitation covenant instead of a non-compete covenant). Also depends on the nature of the business and the conf. info you have been privy to that is not publicly available info. Bottom Line - you may have no choice unless you have another job to go to and have leverage to tell employer that you will leave instead....only you know answers to all these questions. Moreover, if you are an officer of the company then you have greater duties which is problematic in terms of the non-compete.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
The company can require that you sign a legally-appropriate agreement at any time.
A lawyer would need to review the agreement to determine whether it is legally appropriate. If it truly has a post-employment non-compete provision, then that provision is not enforceable in CA, irrespective of where the company is based.
This information does not constitute legal advice and does not establish an attorney-client relationship.