Is it permissible to perform only the post-Dhuhr Sunnah prayer without the pre-Dhuhr Sunnah prayer, without an excuse?

Not performing the pre-salah (qabliyyah) regular sunnah prayer does not necessitate not performing the post-salah (ba'diyyah) one. Thus, a Muslim may pray the post-salah sunnah without the pre-salah one, and vice-versa, or perform some supererogatory prayers without others. However, it is better to maintain all regular sunnah prayers and other supererogatory prayers due to the good they contain, and because they are a reason for Allah's love and a补 (jabr) for any deficiencies in the obligatory prayers.