Did Muhammad descend from Ishmael?

There are some who question the traditional claim that Muhammad descended from Ishmael Abraham's Firstborn, and I can understand why.

The Koran itself never addressed Muhammad's ancestry.  But Islamic genealogies usually trace him to Kedar, but a minority to Nebajoth/Nebaioth, the progenitor of the Nabateans.  These are the first two of Ishmael's sons listed, and Isaiah 60:7 also lists these two together as existing in the Messianic Era.

The Bible seems to always associate the tribes of Ishmael with mainly the region of modern Jordan, but also to an extent the Golan Heights and parts of modern Syria between the Golan Heights and Damascus, and some very far northern parts of Saudi Arabia.  While the parts of Arabia where Muhamamd is traditionally said to have emerged seem more likely to be Keturite tribes or even Joktanite.  In fact the name of Medina probably comes from Medan.

The Nabateans were associated with Petra, a city also linked often to Edom, but also to Kedar in Isaiah 42:11.  Isaiah 21 also confirms Kedar and Tema in the area of modern Jordan, and links Dumah to Seir. It seems like once Edom left the region his ancient lands were all absorbed by the Ishmaelites, I agree with Bill Cooper in After The Flood that the Idumeans were from Dumah not Esau.  Passages like 1 Chronicles 5 also further link Jether and Hagar to the Trans-Jordan region.  The New Testament era Iturians came from Jether.

Jeremiah 49:28-33 is the key.  This is a Prophecy against Kedar and Hazor, in which they are foretold to be scattered by Nebuchadnezzar.

The traditional genealogies of Muhammad do clearly skip many generations.  As they pretty much go right from Kedar to Adnan.  Adnan and his son Ma'ad were contemporaries of Nebuchadnezzar.  Their families fled south when Nebuchadnezzar attacked Kedar, and many tribes of Saudi Arabia, not just the Quraysh from whom came the Hashamites, claimed descent from Adnan.  Like for example  the Banu Kinanah.

Later, around 100 AD the Nabatean Kingdom of Petra was conquered by Trajan and became a Roman Province.  So that is when Nabateans would have fled south.  It was about 400 years before the birth of Muhammad, 170 AD, that the Hubal idol was set up at the Kaaba.  Hubal was a Nabatean god, their form of Baal Hadad, not a moon god as is often claimed.

Things inevitably came full circle as the Royal Family of modern Jordan are the senior heirs to Muhammad.

As far as attempts out there to argue a different ancestry for Muhammad.  Well Muhammad like most people did have multiple ancestors.  But Tribal Identity tended to be determined by Paternal ancestry, and Muhammad's Paternal ancestry going back to Adnan does seem to hold up.  He does also descend from intermarriages between the leading Quraysh and the tribe that controlled Mecca before them, who were possibly a Joktanite Tribe from Yemen.