So you are 18 or 19 (you say born in 2001) and the only ID you have is an original Canadian Social Insurance Number card and a Canadian Birth Certificate (original).
You were born in Canada and obtained a Canadian Passport, moved to US many years ago as a child and Canadian passport expired and lost/destroyed. So you are a Canadian Citizen by birth.
You have never been outside the US since arriving from Canada. You likely completed high school, never worked (as you don't have US Social security number), never had a US Drivers License (never had proper documents to be able to apply for one). If not working, you are likely a college student or unemployed. So you want a US Social security number to be able to work and/or apply for FAFSA (student aid). You want a drivers licence to drive.
How did you enter the US many years ago? On a visitor B2 status? or did your parent say you were a dual US/Canadian citizen, even through you did not have any documents saying you were a US citizen. Since you were a child you likely don't recall. Can you ask either parent?
Now you are applying for N-600 to prove you are a US Citizen by your father being a US Citizen and born out of wedlock.
You need the N-600 to obtain an US Social Security number and obtain a US drivers licence. (and obtain a US passport).
Do you have a long form birth certificate? Most people just have the short form birth certificate. (Name, date of birth, place of birth, birth registration number). Long form birth certificate lists both the mother and father and the attendant who delivered the birth (usually physician).
If not, you should be able request one online from the US, with the registration number of your birth certificate.
If you were born in the Province Of Ontario,
https://www.ontario.ca/page/get-or-replace-ontario-birth-certificate
I don't believe you can apply for a new Canadian passport by mail with what you have. Your original Canadian birth certificate is good, but you need a second government issued ID to verify your identity. Your Canadian Social Insurance number card is not acceptable. Usually Canadian's living in the US will use a copy of their US Drivers Licence or a copy of the US Permanent Resident card (green card), or US passport, a photocopy, signed by your guarantor is sufficient to prove your identity.
Also note you must have photos that meet the Canadian Passport Requirements (50mm x 70mm), if you use a passport photo with US requirements (2" x 2") you will be rejected. You need to find a photographer that is familiar with Canadian requirements.
Also, when you mail in your application is good to use US Postal Service Registered mail to Canada (about $25 and 6 six business days) to track your application to the Passport Office in Gatineaux Quebec. (FexEx or United Parcel Service is more expensive).
Based in the info you provide, it appears waiting for your N-600 is your best way forward at this time. Good luck.