Short answer: Yes. In Jain tradition, Jain Dharma was already present during the times of the Ramayana and the Mahabharata.

Key points from Jain teachings:

• Jain Dharma is anādi-ananta (beginningless and endless). It does not “start” at a particular date; Tirthankaras periodically re‑teach it in every time‑cycle.
• Ramayana era (Rāma-kathā in Jain texts):

- Rāma (called Padma) and Lakshmana are counted among the 63 Śalākā‑puruṣas. - Jain retellings say Rāma remains committed to ahiṃsā; Lakshmana, as the Vāsudeva, slays Rāvaṇa. In the end, Rāma accepts monkhood and attains spiritual progress. - The 20th Tirthankara, Munisuvratanātha, is traditionally linked with this period. - Principal Jain sources: Vimalasūri’s Paumacariya (Jain Ramayana), Hemacandra’s Triṣaṣṭi-śalākā-puruṣa-caritra, and later Jain Purāṇas.

• Mahābhārata era:

- Śrī Kṛṣṇa and Baladeva (Balarāma) are also among the 63 Śalākā‑puruṣas. - The 22nd Tirthankara, Lord Neminātha (Ariṣṭanemi), is Kṛṣṇa’s cousin; his life and renunciation are central in Jain narratives of this time. - Principal Jain sources: Harivaṃśa Purāṇa and Uttarapurāṇa (Digambara), and Hemacandra’s works (Śvetāmbara).

Digambara and Śvetāmbara notes:

• Both traditions agree that Jain Dharma existed in those eras and that Rāma, Lakshmana, Kṛṣṇa, and others are among the 63 great personages.
• Some story details differ (names, sequences, and the final outcomes of certain characters), but the spiritual message—ahiṃsā, self-restraint, and liberation—remains the same.

Essence:

• Jainism did not arise after these epics; it is eternal. The Ramayana and Mahabharata figures are integrated into Jain sacred history with a strong emphasis on non‑violence and the path to liberation.