Here’s how I do a heel or toe on the sock machine:
Instead of cranking around and around to make a tube, I raise the back half (less one on each side) of the needles out of work. So half the needles PLUS one on each side remain lowered/in work.

I have changed colours to make a yellow toe against a natural foot. This is my own sport weight yarn.
Now, instead of going around and around, I go back and forth. And each time that I go back or forth I first raise up one more needle out of work. I raise the first needle that I would otherwise knit first if I hadn’t raised it. (The exception is the first pass in each direction - I raise two needles instead of one. Thereafter, one needle at a time per pass.)
So I am doing one stitch less in each successive row. Or short rows.
I stop when I get to the yellow mark on my cylinder.

This picture is higher resolution and you can click it for closer view.
I’ve pointed out one of the red marks (there is one at 9 o’clock and one at 3 o’clock). The red marks are the point of reference to beginning the short rows, and the yellow marks are the point of reference to end the short rows.
So in this photo I’ve complete my decrease and am about to begin my increase by pushing down one needle back into work each time I knit back or forth. But this time, instead of changing the first needle I would otherwise knit, I push down the needle after the ones that are already down. (If I pushed down the first needle I would hit, I would have to wrap the yarn around that needle first, or I would drop the stitch - still works but takes longer.)

Now I’ve completed the last increase stitch. Remember in the first step I said I raise two needles on the first pass in each direction.
When finishing I don’t push those two down together, but push down ONLY the first (on each side) of the pair. So when I’m finished I have half of the needles up, and half of the needles down (instead of half plus one on each side when I started). The reason for this little manoeuvre is to avoid hole where the completed heel meets the foot of the sock.
Now, the heel or toe is complete so I push down the rest of the needles into work and begin going around and around instead of back and forth.

The first pass is a little tricky and it is important to make sure all the latches of the needles are DOWN, otherwise the needle will drop the stitch.
If you look at the third needle into the natural yarn from the yellow, on the right side. You will see that one latch is up. I didn’t see this !#%!$#&%$#@$ and right after taking this photo I therefore dropped a stitch!
Not to worry - I caught it about 5 rows down and was able to work it back up manually with an extra latch needle.
So that’s the heel and toe story.
It is also possible to do a Scotch Heel on the sock machine. I have instructions on how to do it, but haven’t tried it yet. Looks scary!
Another one that I did try is a double heel and toe. That was ‘interesting’ and perhaps a future blog topic.
And now for a very simple unsock ......

These baby toques were made on my 72 cylinder, with all stockinette (all needles in). I began with the tension quite loose and tightened it up a quarter turn each 25 rows or so. When finished I left along tail which I simply fed through the stitch loops and pulled tight. Finished off with pom poms. These were made with left overs from socks.
Little projects WITHOUT heels or toes are great for using up odds and ends, but ESPECIALLY great when first learning how to use a sock machine.
Lots of tubing experience is a very good thing before tackling those nasty short rows.