In Bala Kanda of Valmiki Ramayan, Vishvamitra's war with Vashishta is mentioned. After his defeat, he leaves for penance and becomes Rajarshi. Indra sent menaka to disturb his penance. Menaka later revealed her true purpose of living with him, he abandons Menaka and his new born daughter Shakuntala to go for another penance and finally becomes Brahmarshi. Markandeya Purana has the stories of Vishvamitra taking the kingdom of Harishchandra who was an ancestor of Rama. Then Viswamitra appears in the court of Dasratha to take Rama and Lakshmana with him to kill the demons of Ravana's army. According to Vayu Purana and Matsya Purana, Ramayana happened in 24th Tretayuga and Mahabharat in 28th Dwapara. My question is whether Vishvamitra was already a Brahmarshi during Ramayana. If yes then can we conclude that Shakuntala and her son Bharata are more ancient than Lord Rama?
In Valmiki Ramayana, the sexual bliss enjoyed by Sage Viswamitra with Menaka was mentioned, but not about the birth of Shakuntala.
विनिःश्वसन् मुनिवरः पश्चात्तापेन दुःखितः || १-६३-१२ भीतामप्सरसं दृष्ट्वा वेपन्तीं प्रांजलिं स्थिताम् | मेनकां मधुरैर्वाक्यैर्विसृज्य कुशिकात्मजः || १-६३-१३ उत्तरं पर्वतं राम विश्वामित्रो जगाम ह |
Oh, Rama, that best saint suspired heavily when he became emotional with reparation. But on seeing the scared celestial wench Menaka, who is shivering and waiting with suppliantly adjoined palms, he sent her away with pleasant words, and he that Vishvamitra indeed went to the northern Himalayan mountain.
However, the result of their conjugal bliss,ie., birth of Shakuntala was mentioned in Mahabharata.
We have to remember that there are many interpolations in Valmiki Ramayana. One such interpolation is the narration of life of Sage Viswamitra. It was discussed in this answer.
However, the main question remains - When did Vishvamitra become Brahmarshi? 24th Tretayuga and Mahabharat in 28th Dwapara?
There is another problem also.
If we negate the appearance of Sage Viswamitra in Bala Kanda, due to assumption of interpolation, then we cannot answer the narration appearance of the Sage Viswamitra in Ayodhya Kanda.
In view of the above narrated issues, we can conclude that Sage Viswamitra belongs to Ramayana period only. He became Brahmarishi in that era .
Mention of Sage Viswamitra in Mahabharata is either an interpolation or that Sage Viswamitra is different from that mentioned in Valmiki Ramayana.