The Veda clearly distinguishes between Shudra and Arya. For example:
A.V., iv.20.4. — “The thousand-eyed god shall put this plant into my right hand; with that do I see everyone, the Shudra as well as the Arya.”
Kathaka Samhita, xxxiv.5— “The Shudra and the Arya quarrel about the skin. The gods and the demons quarrelled about the sun; the gods won it (the sun). (By this act of quarrelling with Shudras) the Arya makes the Arya Varna win, makes himself successful. The Arya shall be inside the .altar, the Shudra outside the altar. The skin shall be white, circular- the form of the sun.”
Vajasaneyi Samhita, xxiii.30 -31— “When a deer eats the barley in the field, the (owner of the field) is not pleased with the nourished animal; when a Shudra woman has an Arya as a lover, (the husband) does not long for (the consequent) prosperity. When a deer eats barley, the (owner of the field) does not approve of the nourished animal. When a Shudra is the lover of an Arya woman, the (husband) does not consent to the prosperity.
Now Arya in Vedas refers to upper castes, and in one case, specifically Vaishya varna. Then Vedas say:
krnvanto vishwam āryam
Make the whole world Arya
So does Veda give any mechanism like specific mantra, puja, sacrifice etc. for bringing Shudra into Brahmin, Kshatriya or Vaishya varnas? EDIT —— Here is another verse from Rig Veda (vi.22.10) varna change
यया॒ दासा॒न्यार्या॑णि वृ॒त्रा करो॑ वज्रिन्त्सु॒तुका॒ नाहु॑षाणि ॥
“Oh, Vajri, thou hast made Aryas of Dasas, good men out of bad by your power. Give us the same power so that with it we may overcome our enemies.” हे (वज्रिन्) ... आप (यया) जिससे (दासानि) शूद्र के कुलों को (आर्याणि) द्विजकुल
How?