If the Mashiach and Olam Haba are so central to our belief why is there no mention of it in the Torah? could it be that it was created later to make people have something to look forward to and to fear when they realised that there is no indication of reward and punishment in this world? after all, if you tell someone he will be rewarded/punished after he is dead there is no way to disprove it. since everyone is afraid of death, this seems the perfect solution and the one adapted by other religions (70 virgins!)
The belief in the world to come is one of the fundamentals of authentic Judaism and is there from the very beginning. You are not the first to ask this question and many of our sages and holy philosophers over the generations have dealt with your question and came up with various answers from different angles all of which are true. The Maharal of Prague [Tiferet 58] explains the reason it is not explicitly mentioned in the written Torah but only hinted to in a few places, since the Torah did not want us to worship G-d for the sake of reward. Similarly did not want to write things that can be promised but not proved [70 virgins…] rather promise things we can see with our eyes and put to test [prosperity, rain etc.] Rav Kook [Orot HaTorah 8:5 based on the Kuzari] adds, that the encounter of G-d down here within the physical realm in the land of Israel and the temple is much greater in many ways than spiritual reward in a world to come, only after the destruction of the temples and exile, the notion of Olam Haba was emphasized since the "real thing" was taken from us.