One (of multiple) ways to do it with SDG2042X and DS1054Z. Connect generator channel 1 (note that channel numbers are arbitrary) output to scope channel 1 input. Connect generator Aux In/Out to scope channel 2. Set scope to trigger mode to Normal, on negative going edge pulse on channel 2, trigger level greater than 0V and less than 5V. Set generator parameters as desired, and in addition under sweep settings, set source (sweep trigger source) to Manual, and Trig Out to On. Then on page 2 of the sweep settings menu on the generator, press the button for Trigger to initiate a sweep. When you press the Trigger button, the sweep starts, and the generator emits a 40uS negative pulse from the Aux In/Out connector on the back of the generator.
You can also set the scope to just trigger off of the same channel it receives the waveform on, however on the SDG2000X generators (not sure how others work), once you set up sweep mode, the generator always outputs a fixed frequency waveform (either the start frequence, stop frequency, or center frequency) on the output channel, and doesn't actually start the sweep until triggered. So you won't be able to get a sweep start synchronized capture by just triggering the scope on the same input (at least not without more complex triggering).