I don't think these are beginner instructions. It takes some skill to do something like that. I have a toe up sock pattern (my own made up one) that starts out with a cast on of 4, increase, and join. But I also have several years experience doing magic loop with circulars. The first few rows are tight. But you have to keep plugging in there. I think the reason for the 4 stitches is to reduce the hole on top. I cast on 4, join, increase stitches, then pull the tail tight to close up the hole at the end of the first row.
For what it's worth, I think the patterns tell you to use 16 inch circulars then switch to double points for the decreases so they can sell you more needles. I use 32 inch circulars for hats and that's because that's the longest one that came with my set. Eventually, I want to get a 40 inch. I use traveling or single loop for the main body of the hat and switch to magic loop for the decreases.