How do I build my cardio capacity for cardiac endurance?? I need to condition my heart for sprinting/jogging?

I haven't done cardio within the last 4 to 5 months, I'm highly deconditioned, I perform hiit for 10 mins and started to get dizzy, I'm on a cutting routine and need to strengthen my cardiovascular system for endurance and of course fat loss, then again I focus on athletic performance. Is long duration cardio good for conditioning? or moderate pace? This question has nothing to do with fat loss, I just need to strengthen my cardiovascular system and eventually after 4 weeks of diligent cardio training, I will engage HIIT for vengeance, I'm on a 12 week program lol, I would like to start HIIT on phase 2 of the program, and that's on november 1st. Is it possible for me to get strong in terms of my cardio system within 4 weeks?