Hey,
That’s your HO, but also the humble opinion of the likes of K. R. Norman. See A Philological Approach To Buddhism where he translates ajata as “without birth”.
Of course that is what ajata, “no-born”, metaphyisically means in the Buddhist sense: without birth, free from birth, and so on. But with such utterances the Buddha also seems to use some Upanishadic style language, almost certainly to provoke his audience. The Upanishadic brahmins use this “Unborn, Undying, Deathless” always with reference to a Self (atta) that is the universal consciousness of Brahman. But by first acknowledging “there is no-born” and then not explaining it as a Self but simply as the escape from the born, the Buddha is first taking the Brahmins along and then actually negating them.
There’s another passage like that in MN140:
Peaceful sages will not be born, will not age, will not die, will not be agitated, and will not long. As there is nothing in them by which they could be born, not being born, how could they age? Not aging, how could they die? Not dying, how could they be agitated? Not agitated, what would they long for?
To copy paste some notes I made a while ago:
When the Buddha says that sages will not die, he at first glance seems to say they will live forever! But he then explains that sages will not die, not because they will live forever, but because they will not be reborn. In other words, they still have one death, but no more after that. The Buddha meant that they will not die again.
The initial confusion is likely intentional, as the passage seems to be a tongue-in-cheek reference to ideas found in the Upanishads which refer to an undying Self, such as: “this is that great Self which is unborn, unaging, undying, immortal, fearless, Brahman.” (BU4.4.25: sa vā eṣa mahān ajātmā ajaro amaro-mṛto-bhayo brahma.) The brahmins believed this Self was eternal, so to them “not dying” did in fact mean living forever. But the Buddha refuted such ideas. Often he challenged ideas through argument or direct denial, but sometimes, like here, by skillfully twisting them around.
A closely connected idea the Lord Buddha adopted with a twist is amata ‘immortal’ or ‘deathless’. It—or rather its Sanskrit form amṛta—is also one of the words in the just-quoted Upanishad, but it already occurs frequently in the oldest Vedas, where it describes the immortality of the gods. This braminic concept of divine immortality is also known to the suttas. In the The Great Steward Sutta (DN19) a brahmin named Jotipaala—Gotama in a past life—asks a Brahma god (whose name was Ever Young, likely not a coincidence given the context): “How can a mortal reach the immortal (amata) realm of Brahma?” But the Buddha’s path, unlike that of the brahmins, does not lead to an immortal heaven realm of eternal youth. So the Buddha used the word amata not in the sense of immortality but in the sense of ‘no more death’ or 'deathless’.
edit: also on the word pada (“state” ??) see this thread which I just started: Is extinguishment (nibbāna) a state? On translating pada