Putting down any landscape fabric, they are all made of nylon a product that does not ever get digested, would not be a good idea, and covering it with something called "topsoil" would not be anything better. "Topsoil" by definition is just the top 4 inches of any soil and unless you know what you want purchasing "topsoil" is more like buying a "pig in a poke" than most people realize, but most of the time is a waste of your money.
As long as the plant you want to get rid of is deprived of access to sunlight, long enough, that plant will die. Some plants roots store enough energy to grow back quite some time after the top growth is killed off, but cardboard or newspaper will work just as well as some expensive landscape fabric, and both the newspaper and cardboard will contribute some organic matter to your soil something which the landscape fabric will not.

I definitely hear you, but... I am considering doing exactly that- blocking the light out for 2-3 years, until all remnants of the grass are killed off. Purchased "topsoil" could be spread on top (or any sort of mulch) which would help exclude light further- while holding the fabric down in during strong wind storms. A cover crop could be planted on top, dug in later etc.

Cardboard.... I tried this several years ago, layered with newspaper. The canary reed too it in stride, if found routes around the cardboard, as well as waited for the paper to decompose before poking through. It is such a huge project large scale- and not guaranteed to work...