Is there a way that I would be able to know if I am pregnant without taking a pregnancy test?

Not right away. You would have to wait until you either missed a lot of periods or started showing to know for sure. And with doing that, the longer you don't know - the longer you would probably go without proper prenatal care.

If you feel the baby move at 16+ weeks you might "know", but you need to take a test sooner then that so you can start prenatal care.

I knew within two weeks of my pregnancy. If you pay attention to your body you will notice little changes like your breast becoming fuller a heavy feeling not the same when you're on your period. But it always helps to take a test if you don't want to go to the doctor there are a lot of over the counter tests such as EPT. You should always go to the doctor's though because you need to take care of yourself and the baby as soon as possible.