If you have a SWEEP HOLDOFF control (it varies the "holdoff" time between successive sweeps), it will delay the sweep long enough that your triggering event is the beginning of the pulse string. Sometimes, on some scope models, there may be an internal jumper that switches the TIME/DIV variable control from that function to the HOLDOFF function.
Another possiblity is to find a "frame pulse", an event that the processor produces at the beginning of the output sequence. If you've programmed the system yourself, if multiple outputs are there, you can program one of the outputs to put out a single pulse right before the output of interest squirts out its data. That becomes your frame pulse.
With a really long data word, the framing pulse becomes really handy in conjunction with the delayed sweep function of a little higher-end scope to give you "microscopic" timing vision.
The only reason that a delayed sweep function might work is that you're adding in a few delays and odd holdoff times that happen to land just right with your signal. If the main sweep won't trigger on something solid, the delayed sweep won't either.
The single-sweep idea, whether with an analog or digital storage scope, will give you a different display each time, although it will be "stable". But after several shots, you might have a picture that's in the right spot on your screen to be useable.
Or, you can build a little one-shot that triggers on your data output at the beginning of the data and has a pulse width that is longer than the data string. The output of this one-shot becomes your frame pulse that you can feed into the external trigger of your scope.
Dean