Actually, it's not a new moon, but a day (tithi) before that, i.e., Chaturdashi which is considered inauspicious birth for a female.
Such a girl is termed as Viṣakanyakā.
This follows from the Skanda Mahā-Purāṇa
Verse 6.1.61.6-10
ब्राह्मणा ऊचुः ।
या कन्या प्राप्नुयाज्जन्म चित्रासंस्थे दिवाकरे
।
चंद्रे वापि चतुर्दश्यां सा भवेद्विषकन्यका ॥ ६ ॥
The Brāhmaṇas said:
- If a girl is born when the Sun is in the constellation Citrā or the Moon in the fourteenth lunar day, she will become a Viṣakanyakā (a
poison girl).
यस्तस्याः प्रतिगृह्णाति पाणिं पार्थिवसत्तम ।
षण्मासाभ्यंतरे
मृत्युं स प्राप्नोति नरो ध्रुवम् ॥ ७ ॥
- A man who grasps her hand in marriage, O excellent king, will certainly meet with his death within six months.
यस्मिन्सा जायते हर्म्ये षण्मासाभ्यंतरे च तत् ।
करोति विभवैर्हीनं
धनदस्याप्यसंशयम् ॥ ८ ॥
- She will render the mansion wherein she is born, even if it be that of Kubera, a place devoid of riches within six months.
सेयं तव सुता राजन्यथोक्ता विष कन्यका ।
पैतृकं श्वाशुरीयं च
हनिष्यति गृहद्वयम् ॥ ९ ॥
- Such is, O king, your daughter who is called a Viṣakanyakā. She will destroy the two families, viz. that of parents and that of her
father-in-law.
तस्मादिमां परित्यज्य सुखी भव नराधिप ।
श्रद्दधासि वचोऽस्माकं हित
मुक्तं यदि प्रभो ॥ १० ॥
- Hence, do be happy, O king, by abandoning her if you have faith in our words, spoken by us for your good, O Lord.
English Translation by G.V. Tagare
So, a girl born on the fourteenth day of the lunar day, and not on the New Moon is considered inauspicious, as per the Skanda Mahā-Purāṇa.