Keep in mind that when humanity actually does begin colonizing other planets in the Halo universe, their fleet waves the flag of the UNSC: The United Nations Space Command, which operates under the Unified Earth Government. In my opinion, 500 years might be a fairly accurate estimation of when this technology would be available to us. We have many restrictions in place to prevent us from advancing technologically at the rate at which we're capable of; war, money, society, lack of resources, etc. Only under a more unified Earth might we be able to extend our galactic borders. Even without those restrictions, developing the technology necessary to travel light-years in the amount of time that UNSC ships can would take decades upon decades upon decades of thought and experimentation.