Here’s a clear, simple view of the question you asked (noting that Brahmi is a script, not a language):

• Tamil: One of the oldest continuously living languages with a very long literary tradition. Early Tamil inscriptions appear around the 2nd century BCE, and Sangam-era poetry (approx. 3rd century BCE to 3rd century CE) is a foundational tradition.

• Sanskrit: An ancient language with deep Vedic roots. Vedic Sanskrit texts date to roughly 1500–1200 BCE, and Classical Sanskrit was standardized later (Panini’s grammar around the 4th century BCE is a landmark). Sanskrit is older than most Prakrits in its earliest form, but later Prakrits developed from Sanskrit.

• Prakrit: A group of Middle Indo-Aryan languages that evolved after Vedic Sanskrit. The emergence of Prakrits is generally dated to well after early Vedic times, roughly in the first centuries BCE and CE.

• Telugu: A Dravidian language with a later literary tradition compared to Tamil, with early works and inscriptions mostly from the medieval period (roughly 10th–12th centuries CE onward).

• Brahmi: Brahmi is a script, used to write many languages (including early Sanskrit, Pali/Prakrit, and Tamil in some periods). It’s not a language itself.

In short:

• If you’re asking about languages: Tamil has the oldest continuous literary tradition among these, but the oldest form of Sanskrit (Vedic Sanskrit) predates many Prakrits.
• If you’re asking about scripts: Brahmi is the ancient script used for inscriptions across several languages, including early Sanskrit and Prakrit.