First time taking probiotics. currently on day 2 taking it. does it cause very mild lower abdominal cramps?

It should cause no noticeable symptoms. Probiotics is just a fancy label for germ colonies that are known to "play nice" or produce no illness inside the gut. If they flourish feeding on the debris left during digestion they can crowd out bad acting germs. Their value to anyone is hard to predict. Most see little benefit to their use. They are a good way to balance the gut after taking antibiotics

Probiotics should not cause abdominal cramps. People often take them for GI symptoms with irritable bowel syndrome and they help those symptoms for some people as opposed to causing symptoms. They can also help counteract the GI symptoms that can occur with antibiotics so they are often recommended to be taken with antibiotics.