You can process the DEM without the streams. The Arc Hydro process will give you a str grid and eventually a DrainageLine polygon layer. These are is where the "streams" are per the DEM (and at the resolution of the DEM)
If I were you, I would start with the Fill Sinks step and move on through Flow Direction, Flow Accumulation, and Stream Definition. At this point I would stop and see if the str grid locates the streams in the right places. If you have aerial photos that you can make out the streams on and they seem to be in the wrong places, you can add a polyline agreestream layer to "train" the DEM. That is basically what burning in the streams does. For example, at a culvert crossing the fill sinks tool will fill in the area upstream of the culvert. The flow direction and resulting str may show the stream going around the culvert. Here you would add an agreestream polyline that will burn a "slot" in the DEM to make the flows align with the culvert. There could be other places that are really flat that you need to define the stream location better.
This could be labor intensive if you have a large area. However, unless you can find a stream layer from some other source, it is what you have to do. Remember, you don't have to have a polyline where every stream is. You only have to have a polyline where the DEM does not correctly define the flow path or stream.
Hope this helps.
