I’ll take your two points separately:

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1. “Where is the archaeological or scientific evidence that we are in Kalchakra?”

From a Jain point of view:

• Kālchakra (time‑cycle), Utsarpini–Avasarpini, 6 ārās, etc. are part of Jain cosmology, described in āgams and later texts.
• These are accepted in Jain tradition as śraddhā / āgama‑based knowledge, not as something proved by modern archaeology or physics.

Modern science today:

• Works with a linear model of time (Big Bang ~13.8 billion years ago, cosmic evolution, geological eras, etc.).
• Has no tools or data that can confirm “we are in 5th āra of Avasarpini in Bhārat Kṣetra,” because:

- Jain cosmology talks of different kṣetras (regions of the universe), - different scales of time (sāgaropama, etc.), - and moral/spiritual conditions (dharma decline, Tirthankars, etc.), which are outside the scope of empirical testing.

So:

• There is no archaeological or scientific “proof” in the modern sense that we are in a Jain Kālchakra.
• It is a spiritual / scriptural doctrine, accepted on the authority of Jinas and Āgams, not on fossils, carbon dating, or telescopes.

If you want a simple Jain explanation of Kālchakra in English, you can read more here

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2. “How are Tirthankaras in the same human shape for the last few billion years?”

A few clarifications from Jain doctrine:

a) Tirthankars are always human – not animals, gods, etc.

• A Tirthankar is always born as a human being, in a human body, never as a deva or tiryanch.
• This is due to the specific Tirthankar‑nāma‑karma that ripens and gives that special human birth and form.
• So “same type (category) of body” = always human, not that the exact biological species is scientifically verified over “billions of years.”

You can see a short definition here

b) “Same human shape” in scriptures does not mean “unchanged biological evolution” in the scientific sense

Jain texts say:

• In different ārās, human height, lifespan, and physical capacities change drastically.

- In early eras, humans are extremely tall and live for vast durations. - In later eras (like ours), they are short‑lived and physically weaker.

• Yet, they are still called “manushya” (humans) – two arms, two legs, one head, etc., a recognisable human form.

So Jain view:

• Form‑category (human) remains fixed for Tirthankars in every Utsarpini and Avasarpini.
• Exact size, lifespan, abilities, environment change with time‑cycle and āra.

This is a religious description, not a fossil record. Jainism is not making a lab‑tested claim that for “billions of years” there is zero biological variation; it is describing a cosmic pattern of human conditions in its own framework.

c) Why so similar across cycles? Because of karma‑law, not random evolution

From Jain standpoint:

• The universe and time‑cycle are beginningless and endless.
• Infinite souls keep wandering in saṃsār under the exact, rule‑bound law of karma.
• When conditions of a particular half‑cycle ripen (e.g., dharma decline, specific āra), exactly 24 souls with Tirthankar‑nāma‑karma take birth as Tirthankars in human form.
• Their inner state (keval‑jñān, passionless, same fundamental teachings – ahiṃsā, aparigraha, anekānt) is identical, even if some outer details differ (names, places, small variations Digambar–Śvetāmbara give in narratives).

So “same type of Tirthankars in same kind of human shape” is explained by:

• Same law of karma,
• Same pattern of Kālchakra,
• Same need: when dharma fades, Tirthankars appear to re‑establish it.

This again is not proved or disproved by archaeology; it is accepted as metaphysical truth within Jain Dharma.

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Summary in very simple words

• Jain Kālchakra and the 24 Tirthankars per half‑cycle are spiritual teachings, not scientifically verified facts.
• Modern archaeology or science has no direct evidence to prove or disprove “we are in this particular Jain time‑cycle.”
• Tirthankars are always human, because Tirthankar‑nāma‑karma always gives a human birth;

but Jain texts also say humans’ size, age, and environment change a lot in different eras.

• Jainism explains the repeating pattern of human‑form Tirthankars over infinite time by karma‑law and cyclic time, not by modern evolutionary biology.

So your skepticism is very understandable from a scientific angle; Jainism simply operates here on a different type of knowledge: scriptural/omniscient testimony (āgama, kevalī‑jnān), not archaeological evidence.