Since you said you're leasing and still paying it off, I'm assuming you have one of the new smart cars... According to the manual, the front passenger seat is able to detect when child restraints are being used (along with the weight of the occupant) and will deactivate the front airbag. I have not tried it myself, but that's how it's supposed to work and I don't see why it wouldn't.
I have not had kids of my own but I helped raise a baby a few years ago and the trunk space in a smart car will not fit any sort of useful stroller. Those things are way bigger than you would think they are, and they usually do not fold into any sort of manageable shape. The biggest problem is usually the wheels on the stroller because they stick out awkwardly from the folded frame that might otherwise fit in a smaller space. Granted, I hear the baby care technology has come quite a bit further since I last bothered to look into the stuff, but I also know it's all gotten bigger too, with increased safety standards.
I've thought about this quite a bit because I intend to have kids in the future and will hopefully be keeping my smart when that time rolls around... but it's really not a suitable car for transporting children except under most dire of circumstances. Like if your baby is sick and you need to drive to the hospital ASAP. You probably won't even need a stroller with you, just the car seat and the bag of stuff - sure, it would work. For everything else I would seriously just recommend a taxi or an uber/lyft to save yourself the hassle because there's just no way a smart will fit everything a newborn needs for an outing. If you have friends or family that live in manageable distance, you can do what we do, and ask to swap cars with them for a day if they don't need the capability of their (likely) larger vehicle. Make sure you both put each other under each other's insurance just to be covered. Bring a blanket to put on their back seat beneath your car seat and a tarp to put beneath the stroller to keep it nice and tidy for them. Poke around and see if there's car shares or coops around if you don't have family or friends you can do the swap with. It's worth it to see if you can go and talk to the company you're leasing from to if they have any backdoor options for people in unusual situations (for example, to keep you as a customer, they might be willing to waive the lease termination fee if you agree to lease one of their bigger vehicles, or something like that).
Best of luck to you!