Kozov,
Here is the reason to assume it is not written by Yonosan ben Uziel:
1. The Gemara says that Yonosan ben Uziel wrote a targum on Neviem but makes no mention of him writing a targum on Torah, which is strange considering how great Yonosan ben Uziel was.
2. There is no mention of Targum Yonosan on Torah anywhere in Shas Bavli & Yerushalmi, or any of the major midrashim.
3. There is no mention of a Targum Yonosan on Torah in the works of the Gaonim.
4. There is no mention of Targum Yonosan on Torah in any of the earlier Rishonim (the Ramban who appears to quote the Targum calls it Yirushalmi, not Yonosan).
5. If Yonosan ben Uziel, a senior contemporary of Rabbi Yochanan ben Zakai, wrote a targum on Chumash, why did Onkelos (a student of Rebbi Eliezer who was a student of R’Yochanan ben Zakai) write one (remember this is before writing Torah shel bal peh become the norm)?
These bits of evidence are not iron-clad, but they are definitely sufficient to rid us of the presumption that it was written by Yonosan ben Uziel.