How long ago was the dreaming supposed to be? If there are great variations due to different versions of the creation myth by different aboriginal cultures, please give a few examples, or the "most notable" one if possible.
The Aboriginal people are protective of their culture, and they do not share all of their stories with the rest of the world. For them, much of what transpired is a private matter, and so only some stories can be accessed. (Aboriginal Dreamtime Stories - Jukurrpa, Gadi Mirrabooka Aboriginal Stories, The Australian Aboriginal "Dreamtime" (Its History, Cosmogenesis Cosmology and Ontology) by Colin Dean)
The idea of the Dreamtime1 is an interesting and complex part of Aboriginal culture. As Wikipedia says, the word was a (mis)translation of an Aboriginal word, alcheringa, also transliterated as altjira. The Dreamtime, however, is not just a past event. It existed thousands of years ago, exists in the present, and will exist far into the future. It is an entity that forms the basis for Aboriginal spirituality, rituals, and history. Another word, tjurjunga, is perhaps a better description of this facet of the concept. (Aboriginal Art Online) However, different tribes have different languages, and so the usage varies across Australia; alcheringa is simply one of the most commonly used terms.
There are many different Dreamtime stories, arising from the fact that the Aboriginal people are not one group, but a collection of related cultures that happen to live on the same continent. This also means that there are many different versions of the same story. (Gadi Mirrabooka Aboriginal Stories)
One big problem is that all these stories are completely separate. The Aboriginal people do not have a single physical "holy book", as some religions do, nor do they have a certain set of deities. Rather, they believe that certain spirits - often nameless - or ancestors were responsible for the creation of certain things in their world. These ancestors can take very different forms - not necessarily human - depending on which people are telling the story. (Australian History - Dreamtime)
There are some specific stories about how certain creatures arose, or how certain features formed. Attempts have been made to correlate these with actual archaeological dates. Unfortunately, there isn't necessarily a connection between when the Aboriginal legends arose and when the things they talk about arose. (Aboriginal Stories) One claim says that some stories go back 65,000 years, making it possible that the stories correctly told of when the creatures were created, if not the actual accurate process. (Gadi Mirrabooka Aboriginal Stories)
All of these stories make up the legends of the Dreamtime, but the creation of the world itself in Aboriginal lore is not connected with all of them.
It is impossible to date all of the different Dreamtime stories, but it seems like you're asking about the actual creation of the world/universe. The exact details of the myth(s) of this period have never been shared with non-Aboriginals, so almost nothing is known about them. There are a few separate answers. Some groups believe that the Dreamtime is/was eternal. This belief goes hand in hand with the idea that the Dreamtime is still occurring. The Gunwinggu follow this belief. Another belief is that the creation happened "a long time ago", or in "the distant past". Most myths are not concerned with an exact date, simply stating that it happened a long, long time ago. (The Australian Aboriginal "Dreamtime" (Its History, Cosmogenesis Cosmology and Ontology) by Colin Dean)
The most comprehensive source I could find on the Dreamtime was The Australian Aboriginal "Dreamtime" (Its History, Cosmogenesis Cosmology and Ontology) by Colin Dean, which was my source for the last paragraph.
1 I'm choosing to use "Dreamtime" throughout the answer to refer to the entire collection of myths, though thanks to competing translations and large language differences, different terms can be used to mean different things.