Hello,

No, it is not possible to apply for the second round of counselling without applying for the first round. Basically second round of counselling is for upgradation. Second round and third round counselling are only for the candidates who wants to upgrade their allotted seat in the previous round of counselling. Also, the candidate who have applied but didn't get any seat in the first round of counselling can apply for the second round.

Hope it helps!

Good luck!