I am not sure but do you have that size of dpns? This is why when I make a beanie I use 2 circular needles the same size. After a bit of knitting you could go to the Magic loop when you have plenty of stitches.
How long are your circs? Pull out the cord about halfway around and scoot the sts toward the tips, folding the work. Then take another needle to join and work the next round. If you just have a longer one in the same size, join with magic loop - pull out the cord and push half the sts toward the needle, loop the R hand needle, fold the work in the left hand and join.
I’m not sure why they told you to CO 4 and [I]then[/I] increase to 8 and [I]then[/I] join the work in round… but whatever. Maybe the writer figured 4 stitches was too few to work in the round without things being awkward?
There are several methods of small diameter circular knitting demonstrated here. Of all of them, my go-to method is Magic Loop (the video demonstration is [I]excellent[/I] and much more effective than any textual explanation), and I’ve started it with as few as 4 stitches (though 8 is much more common). The problem you might run into trying to join in round this way is that the increases you’ve already done might have tightened the existing stitches to a point where it’s tough to get them up the back side of the needle tips. That’s common in top-down hats when you’re just starting out and the increases are close together like that.
You might also be able to CO 4, divide for ML and do the increases with the work [I]already[/I] in the round (though that seems like it’d give you an awfully pointy … point on top) OR, just CO 8 and be done with it. If the purpose of the exercise was to not leave a hole in the top of the hat, you can accomplish this a LOT more easily by threading the CO tail (or another piece of yarn) through the first 8 stitches with a yarn needle (tapestry needle) and pulling the hole closed like a drawstring. That would also avoid the conical point you (might/probably will) get with the 4-stitch CO.
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.
Is the toe start your invention? I’m trying to think how it works so I can try it. I saw a sock pattern for top-downs that ended with pulling the yarn through the last stitches as for a hat and was wondering how to make it work toe-up. I even thought about a provisional cast on and then adding the toe, but I don’t think I like that idea. It is possible for a circ cable to be too long for comfortably MLing I found. I had to tink mittens and wanted to use a smaller needle so I used another cable which was loooong and decided that’s not a good way to go. LOL
My Kninja Master always uses a seamless cast on for toe-up socks. it leaves no holes to close up and no CO bumps to worry your toes either. She showed me how to do it, and I could probably do it again if I thought about it real hard, but I’m not sure I can describe it accurately. As I remember, you just wind the yarn in a figure 8 around both needles with the loop that comes over the top of the top needle slanting knitwise ("") and once you have enough wraps, just pull out one needle and start knitting. Seems like I saw a video for something called “Turkish cast-on” that was similar too – may have been here actually, but I’m not sure. That one can be done on one or two circs, and I think it was invented using two, but somebody figured out a way to do it on one… or something. It’s all kind of hazy now. But that should give you something to Google anyway. Seems like Wendy just called the version she uses a “Figure 8 CO”.
As far as the CO for the hat goes, I’d just CO 8 sts, join and go, then close up the hole by threading the CO tail or another piece of yarn though the CO sts and pulling it shut like a drawstring bag. (I have a pet name for the technique, but it’s a bit … indelicate.)