Finding the manual is a big part of sewing machine maintenance. I would say it's the most important part!
For example, my sewing machine is a thirsty beast. She needs a basic oiling every 20 min of use and every single time I sit down. But if I put oil in the wrong place, it dissolves the rubber and finding a new O-ring the right size is very expensive. If I don't oil enough, then it will quickly wear out. Metal on metal without oil = not good.
But other sewing machines will die if you put a drop of oil in them. They need no oiling at all. They have sealed compartments with grease. They can go for about 5,000 hours between needing deep maintenance.
And then there are some that need some oil sometimes. Once a month? Once a year? Once an hour? And only need oil in specific places. Foot piston? Needle piston? bobbin winder?
Every model is unique. knowing what THIS specific machine needs is a big part of what this badge is about.
So, if you cannot find the manual specific to your machine, you need to find one close enough and explain why you feel that it is close enough and how it differs and how not having the correct manual influences your actions. This is going to be pretty hard to certify and might end up not passing.
Another option is to find a machine with a manual? A friend's machine? Something for $2 at a yard sale or thrift shop? Some libraries lend sewing machines.