Bread is a very old invention, predating agriculture (and was still made by non-agricultural peoples in recent times). We don't know how old. The technologies that are needed are (a) a way to collect grain, e.g., baskets, (b) grindstones, and (c) fire. Of these, almost certainly the most recent is the grindstone. We don't know when the grindstone first appeared, but we know they were in use before 30,000 years ago. Thus, when you ask:

Was this independant?

we can't answer. Even if the grindstone was only invented 30,000 years ago, it's possible that all of the bread traditions outside Australia sprang from a common tradition, spreading from group to group, including to the Americas (leaving Australian bread as an independent invention). However, it's also possible that the grindstone is much, much older than that, and that both African-American-Eurasian and Australian bread traditions have a common ancestor.

Of course, the specific types of bread that are made have evolved as new grains were collected from the wild and, later, farmed, and different methods of cooking developed (e.g., ovens), so we have today much diversity. (And even more diversity if we include noodles/pastas/dumplings and other foods that follow the "take a grain, refine it by grinding it down, and then adding water and other ingredients" procedure.)

For more on the history of bread, see https://www.reddit.com/r/AskHistorians/comments/bvwm17/why_did_ancient_man_create_bread_as_opposed_to/

What made humans decide to cultivate plants and create breads in this way?

Collecting wild grains long predates cultivation. It's quite possible that the first grain-growers thought bread was tasty enough to be worth growing grain for. (A contrary opinion suggests that grain-growing was driven by the desire to have enough grain for beer-brewing.)