We find in Sefer Daniel (11:14): "And the wicked among your people will rise up to actualize a vision, but they will stumble."
Clearly in reference to this verse, the Rambam writes at the end of Iggeres Teiman: “And these are things the prophets have already foretold, and they have told us about what I have told you, that when the time of the true moshiach draws near, there will be many who lift themselves high and place doubts in people's minds, but their claims will not be born out, and they will perish and many will perish with them. And when Shlomo, peace be upon him, made known with his holy inspiration, that this nation when it is sunk into exile will try to arouse itself not at its proper time, and they will die because of this and travails will come upon them – he warned against this, and made an oath against this in an allegorical way, and said (Shir Hashirim 2:7), ‘I adjure you, daughters of Jerusalem…’ And you, our brethren, our beloved – keep his oath and do not arouse the love before it is desired!”
Although the Rambam wrote Iggeres Teiman against a particular false moshiach, in retrospect we see that that false moshiach did not get very far, neither did any other false moshiach in Jewish history. Even the Sabbatean movement’s spread among a large part of the Jewish people lasted less than a year; after that it was a mostly undercover, shunned heresy. The warning of Shlomo Hamelech was clearly referring to the by far most successful false messianic movement in Jewish history: Zionism.
Another verse from the prophets, also quoted by the Rambam in his Letter to Yemen, predicts Zionism. “And Zion said, Hashem has deserted me, and Hashem has forgotten me” (Yishaya 49:14). G-d foretold, says the Rambam, that due to the length and heaviness of the exile, many would think that He had deserted us and removed His face of kindness from us, G-d forbid. But afterwards He testified that He would never leave us and never forget us, as the prophet continues: “Can a woman forget her baby, and not have mercy on the fruit of her womb? They can forget, but I will not forget you.”
“The king moshiach will arise and restore the dynasty of David to its original power. He will build the Temple and gather the dispersed of Israel.” (Hilchos Melachim 11:1) If moshiach will be the one who gathers in the Jewish people, then it is clear that we are not allowed to gather ourselves in before the coming of moshiach.