Is it possible to have endometriosis without first having had a child?

Yes. Yes you can. In fact many women who have endometriosis find out because they have difficulty becoming pregnant. Not all women with endometriosis have pain symptoms. That being said, endometriosis does not always lead to infertility.
Yes. Childbirth doesn't cause endometriosis. Endometriosis can if fact cause infertility. If you have severe cramps or pelvic pain that is not relieved with using things like birth control pills and ibuprofen, you should see your doctor for evaluation.