How can a modified ramjet produce static thrust without a turbine? A big selling point of the ramjet is its absence of moving parts (hence why it can be translated as "statojet" from other languages). However, an even bigger drawback is that a ramjet cannot produce static thrust, thus a ramjet-powered aircraft cannot take off by itself.

The early Leduc 0.22 and Griffon prototypes solved this by adding a coaxial turbojet. This was further refined with the Pratt &amp; Whitney J58 turboramjet that powered the SR-71 Blackbird.

The problem is that by solving the no-static-thrust drawback, adding a turbojet negates the no-moving-parts selling point.

There are missiles that use solid fuel rockets to solve the problem, using the exhaust of the rocket to compress the air in the ramjet, which is sometimes referred as a ramrocket. However, there doesn't seem to be aircraft using this kind of engine, and missile engines have quite different constraints.

Is there an aircraft engine, working or theoretical, that works as a ramjet in cruise mode, can take off on its own power (without requiring ground installations or a detachable first stage/mothership), and doesn't have the many complicated moving parts of a turboramjet? What are its expected characteristics? If not, what are the showstoppers?

And why can't we simply inject some oxidiser (for example WFNA) to produce static thrust?
Well the Pratt &amp; Whitney J58 engines which powered the SR-71 worked in a similar fashion, using a bypass system which allows the engine to operate as a ramjet at high speeds and a turbojet engine at lower speeds.

By the very nature of a ramjet, it relies of stagnation pressure at the intake and inlet throat to pressurize the airflow prior to combustion.  It is just not possible to achieve these kinds of stagnation pressures at speeds under Mach 2 or so.  There was an article in Air &amp; Space magazine a while back about two enterprising Canadian teenagers who tried to fashion a homemade ramjet from iron sewer pipes to power a sled.  They couldn’t get the design to work for this reason.

As such, you would unfortunately need another type of engine to accelerate an aircraft to these fast speeds where a ramjet could work.  Turbojets work well for this application.  So do rocket boosters.  Injecting oxidizer would not be very useful here as airflow through the engine is not fast enough to ensure sustained combustion.