Is it normal to have braxton hicks contractions as early as 23 weeks in pregnancy?

Sometimes. Braxton-hicks contractions can start in the first trimester and get stronger, longer, and more frequent as pregnancy progresses. Sometimes they can be mistaken for labor pains. If you are concerned that you may be in true labor, please call your doctor right away.
Possibly. Braxton hicks contractions are normal during the 2nd and 3rd trimester of pregnancy. So long as they are not painful, are not regular in nature or increasing in frequency, and do not dilate your cervix, they could be entirely normal. But, it is important to know that they are braxton hicks contractions and so it is important to have them evaluated by your ob/gyn.