I would say no..
You said it is your first time of heater use.
I suggest it is just vehicle newness, remember that your heater (like 99% of all cars) is from engine coolant through a mini radiator fin type core inside the center of your dash with air passing through it.
Yes, I would make sure you are heating recirculated inside cabin air, or if outside fresh air is being heated which can include other external odors entering cabin.
I would give it a few more uses and if the smell persists take car to your Mazda Dealer, not a common issue.
2009 Series 2 RX-8 CWP 6MT
2011 NC2 MX-5 6MT