For extra context, I'm a fan of the Iliad and the Olympians gods and recently looked into Robert Graves' "The Greek Myths," which I understand is widely recommended. I was fascinated by his introduction in which he speaks of the native peoples before the Mycenaeans. A people he calls the Pelasgians who worshipped the "Mother Goddess." He goes into some detail about how she was a trinity, even multiple trinities. Nymph, maiden, and crone, or spring, summer, and winter. She was linked with the moon phase due to the female period having a similar time frame and that she led a matriarchal society over all early Greece.
What's more, Graves goes on to suppose that Ionians, Dorians, Acheans (I may forget the particular tribe but I believe he mentions at least three) arrived from the north in waves and slowly influenced the existing matriarchal religion with their patriarchal Olympians. Perseus and the Gorgon, Hercules vs the Amazons, Zeus vs Hera: all subtle clues to the shift in power as the cultures battled.
He's very compelling, especially in his historical fiction where he presents characters living during the culture clash (Hercules My Shipmate, 1944). Mary Renault's "The King Must Die" (1958) also had Theseus living amongst Pelasgian style religion.
I'm told there's little in the way of evidence for much of these ideas. So, long story short, where did they come from?
edited for a plethora of typos.
Graves was obsessed with the notion of the "White Goddess" and with prehistoric female-dominated myth in general. His ideas were influenced by important precursor theories by J. J. Bachofen and J.G. Frazer, among others. His agenda was the matriarchal revision of western myth, especially Greek myth, and in pursuit of this agenda he was both willing and well-equipped to distort ancient evidence and contemporary scholarship.
There is some ancient evidence for "pelasgian" presence in the area which would later be called Greece. There were people living there before the arrival of the Indo-Europeans, and we can know a bit about them. First, numerous ancient sources mention "Pelasgians" in reference to people who pre-dated the "Hellenes." We have no clue what the word means, or what its origins are. Many have tried over the centuries. It was then, as now, a catch-all term for "pre-Greek people in Greece." We should not, however, understand any ancient writer to have any real sense of the pre-Greek world. Even the most perceptive Greeks (Thucydides, e.g.) had no real understanding of the Bronze Age precursors, much less what came before. They had no method of excavating evidence or analyzing artifacts systematically. The Athenians claimed they were autochthonous not because they had any knowledge of prior epochs, but instead because they could clearly see the architectural evidence of those past epochs in their environment: in mycenaean tombs out in their countryside, and the rubble of Mycenaean palace buildings on their acropolis.
Second, there is some scattered archaeological evidence of Neolithic habitation in Greece. For instance, we have some pretty good evidence of habitation in Attica and on/near the Acropolis from as far back as the sixth millennium BCE, much earlier than any "Greek" or even Indo-European presence was possible. The Athenians were right, in a sense: there had been people living in that spot for millennia. Again, the Greeks had no sense of the time scales involved, even if they had the wherewithal to excavate a Neolithic site.
Third, we have some shaky but interesting mythographic evidence for "pre-Greek" myth/religion. Neolithic sites in Greece look a lot like Neolithic remains elsewhere in Europe at roughly the same time, and we can get a vague sense of "Neolithic religion" from the combined evidence. I'm not qualified to talk about that further. But we also think we see traces of interesting vestiges in certain Greek practices which might harken to a much earlier era. Demeter is a good example. The observation of her cult, and especially her in conjunction with Persephone/Kore, has some elements which are seemingly incongruous with other "Olympian" gods (like Athena). Demeter seems different, and some surmise that this difference is a reflection of Demeter being related to some pre-Greek "Pelasgian" origin as a mother/fertility goddess. Check out descriptions of the Thesmophoria at Athens, or the goings-on at Eleusis. For that, see as a start Walter Burkert, Greek Religion, which is conveniently translated to English. Most of the best mythographic work on Greek religion is 19th or 20th century and invariably in very convoluted French or German. The body of evidence for this type of mythographic reconstruction is shaky in the extreme. Often times we are talking about summaries of myths or cult in Christian 6th-century CE sources, drawing on 1st-century BCE poets which are re-tellings of 2nd-century BCE Hellenistic Greek epics, which draw on 6th-century BCE Greek lost hymns, which in turn riff on 8th-century Homeric epic. You get the idea.
So in short: no, there is no evidence for Graves' tri-partite mother goddess, at least no direct evidence.
Based on what you've written in your question, I highly recommend you check out Gibson (ed.), Robert Graves and the Classical Tradition (Oxford 2015), especially chapter 8 ("Robert Graves' The Greek Myths and Matriarchy"), Chapter 9 ("Scholarly Mythopoesis: Robert Graves' The Greek Myths"), and Chapter 10 ("Freedom to Invent: Graves' Iconoclastic Approach to Antiquity"). It is available online via a lot of University libraries. If you can't access it, let me know via PM and I'll try to help you get a look at it.