While the exact date isn't officially announced yet (as of June 18, 2024), the OJEE web counselling for JEE Mains candidates is expected to start in the second or third week of June 2024.

The OJEE website might have a news and updates section where they announce important dates like the counselling start date.

You can refer to the OJEE counselling notification from the previous year (2023) for reference. The start date might be around the same timeframe this year as well.

https://engineering.careers360.com/articles/ojee-eligibility-criteria

I hope it helps!