So far we haven't found a clear and convincing origin for the Spacex Hawk, but I'm rather convinced that somewhere in its DNA it has the Northrop F-5 Freedom Fighter, a successful and relatively economical jet which entered service in the early 1960s. If we disregard the difference in wings and tails for a moment, then the general shape and cross-sections of the fuselages as well as the engine exhausts are very similar.
Next to this, the F-5 was quite an influence in the Anderson universe, in that model kits of this jet were adapted by Derek Meddings' special effects team into the "Arrowhead" fighter aircraft of the World Aquanaut Security Patrol in Stingray. On these, the wings were mounted at the rear of the body, and the stabilisers were used as canard wings toward the front, thus getting us closer to the Spacex Hawk's configuration. The air intakes, modified to fit the canard wings, are now identical to those on the Hawk as well. In Stingray comic strips (as shown below), the TV Century 21 artists often depicted the same aircraft in a slightly more simplified shape.
Above: a good model of an Arrowhead fighter, converted from an F-5 Airfix kit by Kevin Davies.
Below: Arrowhead fighters from a Stingray comic strip by Ron Embleton in TV21 #4.
Staying within the Anderson universe, the Hawk's variable-geometry wings were first seen on Thunderbird 1 in September 1965 (in real life the General Dynamics F-111 was the first production aircraft to have them, which first flew in December 1964). And the Hawk nose isn't far away from that of the Spectrum Angel Interceptor, which first appeared in Captain Scarlet in 1967. But that, unfortunately, is as far as I can take that direction for now.
Possible but probably not
At first glance, an obvious contender for the Hawk origin would be the Nova II craft as marketed in the US by both Tarheel and Durham. Apart from the Thunderbird 2-style tail, the two ships are identical, and the Hawk would then be one of a number of Spacex designs copied from larger toys. But...
As explained in the Copies & Clones section, it's very probable the Nova II may not have existed in time to serve as an example for the Spacex Hawk. Another ship in the Nova series is based on a film prop first shown in the "Thunderbird 6" movie, released middle to late 1968, which would put the development of the Nova series in the exact same time frame as Spacex.
The above is of course assuming that the Nova series was developed together, whereas it could be possible that it was put together from three separate designs where the Nova II already existed awhile longer. Or, since we don't know who actually produced the Nova series, another tiny theoretical possibility could be that it was McArthur who made the Nova series at the same time they produced the first Spacex. And if one of these small possibilities might be true in the end, then the Nova II design origins might just possibly be those described above...