It is not that easy, even if you have a well seasoned garden.
I have grown potatoes that method twice, it works but , now this depends on what you want, your yield is reduced, but it does work.
You will need a constant supply of hay or straw, and I saw a hay stack of bales in the back of her garden.
When I used bales every year, depending on if I used them on the whole garden or just part, it would take from approx. six to a dozen every year.
The hay does not just stay on top of the garden as hers seems to indicated, it rots and turns into soil.
A deep loose covering will take a dozen bales on a approx. 24 x 12 garden area.
Just slicing squares off of a bale will last longer but it will take more bales.
If you have a large trailer or know a farmer well, one or two of the LARGE square bales might actually work here.
You can have large slices that cover a lot of ground or just shred off of the bale as you need it, plus they would store fairly easily and could be decorated with pumpkins, scare crows etc. for Halloween and Thanksgiving.
The soil underneath is not loose unless you loosen it up with a tiller.
Her garden was the work of decades, so do not ever think, unless you inherit a well worked garden that yours will look like that quickly.