Your answer is self defeating. Unborn means eternal. The unborn existed before the phenomena came and passed. The unborn existed before the temporary "state of mind" you refer to as liberation (lol).
Your whole world of ideas are just within the realm of fantasies.
Ajāta means not jāta. Here is the definition of jāta from the
Pali Text Society:
Jāta
Jāta [pp. of janati (janeti), cp. Lat. (g)nātus, Goth. kunds; also Gr. (kasi/ -- ) gnhto/s, Ohg. knabo] 1. As adj. -- noun: (a) born, grown, arisen, produced (=nibbatta pātubhūta Nd2 256) Sn 576 (jātānaŋ maccānaŋ niccaŋ maraṇato bhayaŋ); jātena maccena kattabbaŋ kusalaŋ bahuŋ Dh 53=Miln 333; yakkhinī jātâsi (born a G.) J vi.337; rukkho j. J i.222; latā jātā Dh 340; gāmanissandhena jātāni sūpeyya -- paṇṇāni Vism 250. -- (n.) he who or that which is born: jātassa maraṇaŋ hoti Sn 742; jātassa jarā paññāyissati J i.59; jātaŋ+bhūtaŋ (opp. ajātaŋ abhūtaŋ) It 37. -- (b) "genuine," i.e. natural, true, good, sound (cp. kata, bhūta, taccha& opp. ajāta like akata, abhūta): see cpds. -- 2. As predicate, often in sense of a finite verb (cp. gata):
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born, grown (or was born, grew); become; occurred, happened Sn 683 (Bodhisatto hitasukhatāya jāto); bhayaŋ jātaŋ (arose) Sn 207; vivādā jātā Sn 828; ekadivase j. (were born on the same day) J iii.391; aphāsukaŋ jātaŋ (has occurred J i.291. -- So in loc. abs. jāte (jātamhi) "when . . . has arisen, when there is . . .," e. g. atthamhi Vin i.350=M iii.154=Dh 331; vādamhi Sn 832; oghe Sn 1092; kahāpaṇesu jātesu J i.121. -- 3. ˚jāta (nt.) characteristic; pada˚ pedal character S i.86; anga˚ the sexual organ Vin i.191; as adj. having become . . . (=bhūta); being like or behaving as, of the kind of . . ., sometimes to be rendered by an adj. or a pp. implied in the noun: cuṇṇakajātāni aṭṭhikāni (=cuṇṇayitāni) M iii.92; jālakajāta in bud A iv.117; chandajāta=chandika Sn 767; sujāta Sn 548 (well -- born, i. e. auspicious, blessed, happy); pītisomanassa˚ joyful & glad Sn p. 94; J i.60, etc.; gandhajāta a kind of perfume (see gandha). Often untranslatable: lābhappatto jāto J iii.126; vināsa -- ppaccayo jāto J i.256. -- 4. a Jātaka or Buddhist birth story DhA i.34.
-- āmaṇḍa the (wild) castor oil plant VvA 10; -- ovaraka the inner chamber where he was born VvA 158; J i.391 (so read for jāto varake). -- kamma the (soothsaying) ceremony connected w. birth, in ˚ŋ karoti to set the horoscope PvA 198 (=nakkhatta -- yogaŋ uggaṇhāti); -- divasa the day of birth, birthday J iii.391; iv.38; -- mangala birth festival, i. e. the feast held on the birth of a child DhA ii.86; -- rūpa "sterling," pure metal, i. e. gold (in its natural state, before worked, cp. jambonada). In its relation to suvaṇṇa (worked gold) it is stated to be suvaṇṇavaṇṇo (i. e. the brightcoloured metal: VvA 9; DhA iv.32: suvaṇṇo jātarūpo); at DA i.78 it is expld by suvaṇṇa only & at Vin iii.238 it is said to be the colour of the Buddha: j. Satthu -- vaṇṇa. At A i.253 it is represented as the material for the suvaṇṇakāra (the "white" -- smith as opp. to "black" -- smith). -- Combd w. hirañña Pv ii.75; very freq. w. rajata (silver), in the prohibition of accepting gold & silver (D i.5)≈ as well as in other connections, e. g. Vin i.245; ii.294 sq.; S i.71, 95; iv.326 (the moral dangers of "money": yassa jātarūpa -- rajataŋ kappati pañca pi tassa kāmaguṇā kappanti); v.353, 407; Dhs 617. -- Other passages illustr. the use & valuation of j. are S ii.234 (˚paripūra); v.92 (upakkilesā); A i.210 (id.); iii.16 (id.); -- S i.93, 117; M i.38; A i.215; iii.38; iv.199, 281; v.290; J ii.296; iv.102; -- veda [cp. Vedic jātaveda=Agni] fire S i.168; Sn 462 (kaṭṭhā jāyati j.) Ud 93; J i.214; ii.326= iv.471; v.326; vi.204, 578; Vism 171; DA i.226; DhA i.44 (nirindhana, without fuel); -- ssara a natural pond or lake Vin i.111; J i.470; ii.57.
Nothing here about ajāta meaning "eternal."