There is not an explicit mention of an Aryan invasion in the Hindu texts

Aryan Invasion Theory (history and controversies)
From Wikipedia, the free encyclopedia Main article: Indigenous Aryan Theory

Some Hindu thinkers like Sri Aurobindo reacted against the Aryan Invasion theory on spiritual rather than historical grounds, claiming them to be "materialistic." Sri Aurobindo interprets the descriptions of war in the Rig Veda often as descriptions of spiritual warfare or as nature-poetry. He also warned against the misuse of the theory: "So great is the force of attractive generalizations and widely popularized errors that all the world goes on perpetuating the blunder talking of the Indo-Aryan races, claiming or disclaiming Aryan kinship and building on that basis of falsehood the most far-reaching political, social or pseudo-scientific conclusions."[44]

Some Hindus have emphasized the fact that there is not an explicit mention of an Aryan invasion in the Hindu texts. Aurobindo thus writes: "But the indications in the Veda on which this theory of a recent Aryan invasion is built, are very scanty in quantity and uncertain in their significance. There is no actual mention of any such invasion..."[45] Also Vivekananda[46] remarked: "As for the truth of these theories, there is not one word in our scriptures, not one, to prove that the Aryan ever came from anywhere outside of India, and in ancient India was included Afghanistan. There it ends."

In modern India, the discussion of Indo-Aryan migration is charged politically and religiously. The debate has produced a lot of polemics on both sides.[47] Supporters of migration are faced with several accusations. The major one is that the British Raj and European Indologists from the 19th century to the present day promoted the Aryan Invasion hypothesis in support of Eurocentric notions of white supremacy. Assertions that the highly advanced proto-Hindu Vedic culture could not have had its roots in India are seen as attempts to bolster European ideas of dominance.

sites critical of the Aryan Invasion or Migration Theory
A Fresh Look at Ancient Indian History - By B. B. Lal - Director General (Retd.) - Archaeological Survey of India
Aryan Invasion Theory (hinduwisdom.info)
The Aryan Invasion Theory and Hindu Politics By David Frawley (dharmacentral.com)
Aryan invasion theory - David Frawley (stephen-knapp.com)
Overview on the Aryan Invasion Theory by Stephen Knapp (stephen-knapp.com)
The Riddle of India’s Ancient Past, Vedic roots of early Tamil culture Michel Danino (voiceofdharma.com)