Unless your server supports some functionality to provide this, I don't think you can get something from the stream without connecting to the stream.
You presumably already have some solution which will connect, get a frame, and then disconnect, I am guessing. In case you are not aware you can also do this via ffmpeg with the following command, although I am not sure what the bandwidth overhead is or how it opens and closes the connection under the covers - you would need to experiment with it to see:
ffmpeg -y -i rtsp://your_rtsp_strea -frames:v 1 output.jpg
Its worth noting that the codec in use will affect the number of frames you need - simple codecs or codec profiles will encode each frame separately, but others will have reference frames every, for example, 10th frame and the frames in-between will be encoded as a delta to the reference frames. Hence, you need to actually get the previous and sometimes even the next reference frame in addition to your target frame to actually extract the image.
If your stream is available in DASH or HLS, then you also have the option to just download a single segment - these protocols will already have broken the video stream into multiple segments, typically somewhere between 2 and 10 seconds long. However, you do need to make sure you download the segment from the bitrate that you need - these protocols will have multiple bit rates streams to allow for different resolutions and network conditions.
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