The British car designed to go 1,000mph (1,610km/h) will make its first public runs in Cornwall later.
Bloodhound SSC is conducting initial "slow-speed" trials and should get up to about 200mph (320km/h) on the runway at Newquay Airport.
Driven by RAF Wing Commander Andy Green, the car aims to break the world land speed record in 2019.
This will take place on a special track that has been prepared on a dried-out lakebed in Northern Cape, South Africa.
"This is about showing the world what we're about," said Wing Commander Green.
"We've designed and built the most extraordinary, sophisticated, high-performance land speed record car in history. It will do 0-200mph in about eight seconds. For a five-tonne vehicle - that's eye-popping performance," he told BBC News.
It is exactly 20 years since the RAF man drove the jet-powered Thrust SSC vehicle through the sound barrier in the American Nevada desert to register a speed of 763mph (1,227km/h).
His new machine benefits from two decades of technological improvement and will have the assistance not only of a state-of-the-art Eurofighter-Typhoon jet engine but the thrust of a rocket motor.
Bloodhound seeks in the first instance to push the existing record above 800mph, but then wants to reach a speed that no-one is ever again likely to want to try to match.
The sleek, arrow-shaped car has taken some 9 years to develop and still awaits its Norwegian rocket motor.
Nonetheless, it is now at a stage where it can begin slow-speed trials, to test the performance of the Eurofighter power unit, and to run the rule over the vehicle's steering, brakes, suspension, and electronics systems.
The shortness of Newquay's runway (1.7 miles/2.7 km) severely limits the speed Bloodhound can attain before it needs to brake and safely stop. However, the thousands of ticketed spectators should still get a good sense of the car's potential. (Thursday is now a closed event; no further tickets are available. Some are still available for Saturday, however.)
Along with the absence of the rocket motor, the other big difference from the race set-up of Bloodhound is the wheels. For Thursday's runs, these will be thin, rubber-shod discs; the tyres are actually refurbished Dunlops from 1960s-era English Electric Lightning jet fighters.
Rubber works fine at slow speed on a concrete Cornish runway but would be useless in a record attempt where they would instantly shred as the wheels turned at something over 170 revolutions per second.
In South Africa, Bloodhound will use all-aluminium discs instead.
The project team - which includes Thrust SSC director Richard Noble and aerodynamicist Ron Ayres - had initially hoped to be on Northern Cape's Hakskeen Pan back in 2011.
But technical challenges have stretched the schedule. It took five years, for example, just to find a shape for the car that could achieve the desired speeds and run stably along the ground and not flip up.
And sponsorship difficulties have also been a source of delay. Bloodhound's development can proceed only at the pace permitted by the flow of cash coming into the largely private project.
But Mr Noble says Thursday's running should be proof that plans are firmly on track.
"In 2018, we've decided we're going to run the car really fast. There are all sorts of variations on this in terms of the engineering fit and the location but it might be 600mph or 700mph," he told BBC News.
"Hakskeen is the preferred place. The South Africans have been incredibly good to us."
Watch videos of Bloodhound supersonic