I don't have axis account but had Flipkart axis CC when I applied.
Are you applying via Airtel app?
For me, the Airtel app was showing no offer/the application page never came up,
I then tried with installing Airtel app on family member mobile and surprisingly for them application page opened up, where I filled my details (PAN, name) and keeping mobile contact number of family member and it was approved. After receiving card I updated mobile number to self.
May be give this a shot, if not done yet, ofcourse keep in mind cooling period.