Absolutely it can be normal to get back pain so early on. Most of the changes in your body happen in the first trimester (which is why it is also the trimester that makes you most tired!). Your hormones are changing rapidly which start allowing for the laxity of your ligaments. As they start changing so too does your pelvis (even though you may not be showing or thinking thats it changing!).

The other reason can be due to the fact that before you even became pregnant, you may have been holding onto some compensation in your back or pelvis (which would have eventually become painful) and the pregnancy has exaccerbated it leading to pain.

All of these reasons can be easily treated - but the main point is to let you know that you are not abnormal..... and more importantly, that just because you are feeling back pain so early on that it will necessarily become worse later in the pregnancy!