Hi,
According to the Notification for 2018-23 admission notification "Candidates who are likely to complete standard XII/HSC or equivalent by the end of June 30 can also apply, Subject to meeting the eligibility criteria as mentioned..."

As you have said that your original report card will be out only by the second week of July this could play spoiler in your case but I was going through their site and found that it does provide Provisional admission to students. If you cleare all the hurdles with flying colors and provide the provisional certificates then you may also be given provisional admission. I hope it helps!