It sounds like you are talking about a "bursty" transmission. This is common in real-world communications systems (for example, WiFi and Bluetooth operate this way).
What you say is exactly right - relying on power levels alone is not a reliable way of detecting a transmission. A real-world bursty communications system solves this problem by inserting some amount of completely "known" signal into every transmission. This carries no payload information whatsoever - it is specified by the communications standard (so both the transmitter and the receiver know it) purely to aid reception.
In many cases, this known redundant signal is inserted somewhere at the start of the transmission, in which case you might see it referred to as a "preamble". (However, in unusual cases, like TETRA which is what the police radios use in much of Europe, a "midamble" is used instead). In other contexts, this kind of known signal might be referred to as a "pilot" or "training sequence".
Although it might seem wasteful to transmit this redundant signal, it turns out to be very useful - not only for detecting a transmission, but also for performing other tasks that improve the reception (such as timing synchronization, frequency correction, gain control and channel estimation).
Therefore, if you have control over the data that is being modulated, then you should try putting some known data at the front of every transmission. Then, at the receiver, (in the simplest case) you can correlate using this known sequence in order to reliably detect the transmission. There is quite a lot of study behind how to choose a sequence that will produce really reliable detections in different scenarios. You could read about M-sequences, Gold sequences, Hadamard codes, Barker codes and many more.
If you don't have control over the transmissions, then you need to find some information about them. If you really know nothing about their structure, and can't estimate anything, then unfortunately power level detection may be the best you can do.