I'm not sure if this is true, if the missile is coming head on. If it is made in a stealthy way, the "head" of the missile could obscure the engine area and make the plume invisible to the target. Having low RCS alongside with hidden plume could make a passively targetted missile relatively stealthy to the target.
Ofcourse, anyone with enough offset to the target would be able to easily detect the engine and thermal release but the target could be unaware.
Another method to hide it is if missile uses some kind of obstacle in order to accelerate behind, for example you fire your missiles and they accelerate when a moon or a planet break line of sight from the target to the missiles. This would make their acceleration burn invisible to the target and could get them very close without being noticed.