Errmm, the answer is plainly yes. It would just have had to include predictions for each year of the next few thousand. And make it meteorological predictions to avoid self fulfilling prophecies. Also, if it had contained detailed instructions on how to build a space ship rather than a mishcan.Now I'm assuming that the space ship comment was written tongue-in-cheek. But if not, I would discount this as a "proof from God". After all, if the raison d'etre of Torah is to be an "instruction book for living", why would God include such things that were irrelevant for such a purpose? Yes, a blueprint for some advanced technology would argue for a superior life form, but a rationalist/skeptic would likely claim that it was the product of an alien author rather than the Creator of the Universe! [As an aside, the intentional inclusion of scientific data now known to be erroneous is one of the main reasons that we know the Urantia Book was fabricated by a human author(s) who relied on the science of his time. Oh wait, the Torah also includes the "science" of its time (e.g., the Creation story and the Flood story) that we now know are not scientifically true. Dang! Well at least we can allegorize the Torah stories or rely on "non-overlapping magisteria"...]
But let's grant anon's assumption and disregard the question of why God would include material whose only function were a proof of His authorship. Besides, a midrashic tradition would certainly produce a rich corpus and apply ethical teachings to such proof-texts. Let us also ignore Clarke's 3rd Law (any sufficiently advanced technology is indistinguishable from magic) and assume that most folks would default to the God explanation rather than that of a super advanced culture. So posit that the Torah is exactly the same as we have it now, but with the addition of a very long Parashat Mezeg Avir (whose reading would be on a Yom Tov with either fasting or plenty of shnapps!) that contains meteorological predictions for each year of the next few thousand years.
At first, I thought that writing the Torah so that it was undeniably written by God would violate a core principle of Judaism, that of the imperative for free-will. After all, if folks KNEW with 100% certainty that God wrote the book, they'd be so much more likely to follow it. However, even leaving aside the rebellion stories (Golden Calf, Korach...) that some like to point to in countering this assertion, I realized that nothing would really change from what we have today. The difference would be in the details.
Tanach would be filled with stories written by "meteorological neviim". The influence of the priestly caste - with their claim to exclusive use of divine weather instruments (wind gauges, crude thermometers) - would wither after the destruction of the Second Temple. They would be supplanted by the Pharasaic rabbinic tradition who would use hermeneutic principles to expound the many faces of Torah behind each weather prediction. An unbroken chain of tradition would eventually give rise to gedolim who were well-versed in cloud formations, but also involved with creating tznius patrols to dictate the color and length of foul weather gear, and proclaiming bans on books (the Modern Orthodox Farmer's Almanac) and TV (the Reform Weather Channel.)
Of course, Judaism would still be a minority religion since the "offshoot religions" of Christianity and Islam would accept that the "Old Weather Testament" was God-given, but that its proscriptions were supplanted by later and more-perfect revelations. The former would give rise to many climate sects (the Temperates, The Tropical Evangelicals) and various end-of-day messianic cults (we'd be close to the end of the 3000 years of weather predictions so there would be plenty of 2012-type wackos).
We'd still have OrthoFundies that believed every word was from God and was literally true. Countering them would be adherents of the JEPDW Documentary Hypothesis (the "W" being the "Weather Document".) We would also have some Orthodox scholars (sorry, I mean Orthopraxic Heretics) a la James Kugel that would argue for a prophetic tradition mediated by a lesser divinity like Af-Bri!
In one of my earliest posts I asked, "if you consider yourself an atheist or agnostic what would be sufficient proof to you for the existence of God?" In a similar vein, what would be sufficient proof to you for the existence of a God-given document?