You say: " I never did the two authentication process"
If you never signed up for two factor authentication then you are likely still using security questions. Do you know if this is indeed the case? If yes, then answer the security question(s) when asked.
This Apple article has instructions for what to do if you have forgotten your Apple account password —> If you forgot your Apple ID password - Apple Support
or go directly to this link —> http://iforgot.apple.com/
If you didn't receive your verification or reset email, read this Apple Support article: If you didn't receive your verification or reset email - Apple Support
"When you make certain updates to your Apple ID, we’ll send you an email to help you complete the update. For example, you might have reset your password, reset your security questions, or added a new email address to your account."
If you are indeed using two factor, have forgotten your password, and do not have access to a trusted device or telephone number to receive verification codes, you can request account recovery (read this support article: How to use account recovery when you can’t reset your Apple ID password - Apple Support ) to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity.