Well, if you're saying one god (sorry for nitpicking, but you said a god). In my Kemetic/ ancient Egyptain beliefs, your soul has five parts: the Ba (our personality), the Ka (life force that leaves your body), the ib (the heart/record of good and bad deeds), the Ren (all your experiences and such), and the Sheut (also known as your shadow, can be used to bring back the other parts). So, people can have more than one god and have a idea of a soul. And some (the ones we learn about) Buddhists have no gods but believe in souls.
I believe that humans are spiritual beings and that you don't have to believe in god to be spiritual. Religious isn't necessarily spiritual, right? So does there have to be a god to be spiritual? No, I don't think so. But that's just my own humble opinion.
no, everything has a spirit/soul, whether or not you believe in a god. There are some beliefs that don't believe in any gods or higher beings but believe in souls. Priest of Anubis put it very well lol.