Permission to build the 30 metre dish was first granted in 2011, but legal objections and demonstrations have held up construction since then.
Final approval was given last week.
There are already some observatories on top of Mauna Kea mountain, but it is the size of the proposed telescope and its proximity to ancient burial sites that have angered opponents.
Mauna Kea, at 13,800 feet is the highest peak in the Pacific, and is regarded as sacred by some island inhabitants and represents ancestral ties to creation.
The summit is believed to be the meeting place of Papa (Earth Mother) and Wakea (Sky Father), the progenitors of the Hawaiian people.
It is also both a burial ground and the embodiment of ancestors that include Na Alii and Kahuna (high ranking chiefs and priests.)
Activists say they will hold more demonstrations against the telescope project when construction equipment is moved onto the site on Monday.
Governor David Ige said unarmed National Guard units will be used to transport personnel and supplies and enforce some road closures, but they will not be used in a law enforcement capacity during planned protests.
“We just are asking people to be safe … we certainly would ask that they be respectful of those who have to work on this project,” Ige said.
“We certainly are being respectful of those who choose to voice their disagreement with the project we understand that that’s important as well.”
However protester Rhonda Vincent said closing the road to the mountain would be like blocking access to a church.
“If we can’t access our own gods, our own spirituality, isn’t that wrong?” she said.
Not everyone objects to the building of the new telescope, with some saying it will bring many economic and educational benefits.
At 30 metres across, the diameter of the primary mirror will be three times greater than the world’s largest existing visible-light telescope.
Mauna Kea was chosen because its summit is above the clouds and provides a clear view of the sky with very little air and light pollution.
Astronomers say it will allow them to reach back 13 billion years to answer fundamental questions about the advent of the universe.