Not possible because you don't know the exact flow velocities and discharges at different flow depths of the crosssection. Although you don't know velocities and discharges you may calculate the discharges at different flow depths assuming uniform flow that you can use Manning. But dont forget that this assumption is not true....
Agree, not possible, especially for research level accuracy. I uploaded a couple papers that mention accuracy of DEMs for stream georeferencing, and James et al compares in figure 4 a topographic map with LiDAR coverage. LiDAR pulses are absorbed by water, but if one has clear water, green LiDAR could give some depth estimates. Many rivers are not wadeable, some not boatable, so hiring a professional firm with the right equipment is probably the least expensive alternative for quality stage discharge development for one river. It is important to remember, most rivers adjust through time, so perfection may never be achieved. The Doppler instruments are probably most accurate and easiest to use for larger rivers. Many hazards or issues can occur with high flows as sediment, floating wood or other debris, bedload, etc., and sometimes these extreme flood flows are estimated based on elevation markers, extending flow duration curve and possibly other tools as HECRAS, Manning, etc. For research level work. rating curves are dependent on quality cross section and flow measurements. Small streams might be gauged with more accuracy with weirs, flumes with dimensions that have been rated and installed to specs. There are various ways to obtain rough velocity measurements and some as simple as timing the rate that dispersed oranges move from one channel location to the next. But this is not research grade work. Injecting fluorescent dye might be useful, but sampling becomes difficult at the river scale, as not all the water flows at the same velocity.
If you have a fine enough DEM for couple of mills upstream and downstream of a point. And you assume "steady state" and start with a hypothetical small Q upstream and increase it smoothly (with a slope way smaller than your numerical solution time step), then you solve fully dynamic Saint Venant equation (Shallow Water Wave) in 2D. You can find the elevation of water surface at the given cross-section of your river. Just consider that the reach you are modeling must be long enough so your upstream BC and downstream BC do not pollute the water elevation at that point of intreat, as a rule of thumb assume you need 20 times of your river width up/down stream.
By the way: you can do this in SMS with SRH2D, just add a "monitoring line" and read the Q once and read the WSE next time for a similar run.