Its Rolls-Royce EJ200 turbofan has been slotted into the vehicle's upper-chassis for the first time.
Engineers need to check the power unit will sit comfortably inside the car with the correct clearances.
The EJ200 is normally seen in a Eurofighter, but Bloodhound will use the engine to help it break the world land speed record (763mph) and then raise the mark beyond 1,000mph.
The project is currently on course to try to achieve the first stage in this double quest at the end of the year.
Major components are in the process of being manufactured with some of the UK's top aerospace companies.
As soon as these parts arrive at Bloodhound's technical centre in Bristol, they are bolted in place.
The UK Ministry of Defence has loaned three EJ200s to the project. These are early development models that have no combat use.
The Rolls-Royce units develop about 20,250 lbf (90 kN / 9 tonnes) with reheat. This on its own, however, is not enough to push Bloodhound into the record books.
The EJ200 will be used to get the car rolling. Once it reaches 350mph, a Jaguar V8 engine will accelerate, a clutch will engage and nearly 1,000 litres of HTP oxidiser will be pumped into a catalyst pack, bringing a rocket on stream.
It is the combined thrust of the EJ200 and this booster - produced by Nammo in Norway - that will propel Bloodhound through the sound barrier and on to speeds never before achieved by a land vehicle.
All of the jet thrust is reacted through a single hollow thrust trunnion (fixing) just 32.5mm in diameter, with a wall thickness of only 3.25mm. The EJ200 hangs from this mounting point.
Although Bloodhound SSC is nearly 13m long, space inside the car is at a premium, and the clearance between the EJ200 and the chassis in some areas is a mere 10mm.
The EJ200 intake cannot cope with an airflow of 1,000mph (1,610km/h). This rush of air could damage its fan blades.
So the car's designers have shaped the car's cockpit to create a series of shockwaves that slow the air down to 600mph (965km/h).
While the jet engine will be comfortable with this, the same may not be true for driver Andy Green. The noise this maelstrom of air makes will be immense.
The car's upper-chassis - which houses the EJ200 - is made from aluminium machined ribs with titanium stringers.
The titanium skin is held together by 11,500 aerospace grade rivets - everyone hand fixed and polished - and also bonded with special glue.
It would be sufficiently strong with either rivets or bonding, but the Bloodhound engineers have combined the two for extra security.
The project expects to have the finished car on the runway at the Newquay aerodrome in Cornwall for shakedown tests in August.
Assuming this goes well, the vehicle will then be shipped to South Africa to begin its record bid using a "race track" that has been prepared on Hakskeen Pan, a dried out lakebed in Northern Cape.
Andy Green set the current land speed record in the Thrust SSC vehicle in the Black Rock Desert in Nevada, US, in 1997.
The RAF Wing Commander is one of three central figures from that earlier venture working on Bloodhound. The other two are project director Richard Noble, and chief aerodynamicist, Ron Ayers.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos
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