It was a common technique with analog 'scopes to put them into auto trigger,so that they would "free run", tracing a line across the screen.
In DC coupled mode, this was very useful for quick checking of DC supplies, or for adjusting DC voltages for a maximum ot minimum value.
It sounds like this is what you want to do.
Early DSOs that I used did not have an equivalent "free run" function, so we had to try to use the "roll" mode, which was pretty useless, as it wanted to display the DC variation as a slow waveform, making it very difficult to see variations in level to adjust things.
Modern DSOs do have such a mode, so can probably be used in the same way as an analog instrument
(I do not have any type of DSO, either old or new, so the comment about modern ones is based on what I have read in this forum & others).