Can the Pentateuch be both Mosaic in origin and sixth century?

Yes, it can be because the Pentateuch was written in third person point of view yet originated from Moses. The writing/s was probably in the sixth century because of some implications from the books which called “anachronisms.”

 The Pentateuch contains the writings of Mosaic origin and the sixth century scribe/s handwritings.  it contains the Book of the Law, Covenant, curses and blessings, and wars that had been recorded by Moses’ authority given by God in his time as God told him to do so (Ex. 34: 27, 28; Ex. 24: 7; Num 5: 23; Ex. 17: 14; Numbers 21: 14) and the words of the writer/s who wrote the Pentateuch in third person that can be dated in the sixth century when after the kings of Israel as critical scholars claimed because of the anachronisms as found in Gen. 36: 31.

In reading the verses above, it is clear that Moses and others under his command wrote books. Moses wrote a book of “wars” and “covenant” (Ex. 17: 14; 34:27, 28; 24:7) while the priest wrote the book of “curses” (Num. 5: 23). However, the Israelites tradition called all those writings as “Book of Moses” (Ezra 6: 18; Neh. 8: 1; 13: 1).  In Ezra’s and Nehemiah’s time they mentioned their use of the book of the Law of Moses. It appears that the book of Moses still existed in their time. It appears that the writer of Pentateuch took all the “Book of Moses” as his main reference and had quoted directly. Beside the book, the writer had used also “oral” sources originated from Moses like Moses’ speech in Deut. 9 and the following chapters because Moses doesn’t need to communicate in letter with them for he was with them. The writer of the Pentateuch had written the content of the “Book of Moses” and the oral words of Moses into narrative form as Doctor Mac said, “Moses was the source.” Thus, the Pentateuch is Mosaic in origin but also contains the handwriting and words of narration of the sixth century scribe/s that compiled them and filled them more with information about the creation, patriarch, and the Israel Journeys from Egypt which the laws and book of Moses didn’t mentioned which probably from other minor sources.