"stream burning" lots of links on this.
ArcHydro has conditioning tools, but for a quick solution,
Take your river (polyline or polygon I presume).
convert it to raster with the exact same cell size, extent, snap raster as your dem.
assign where the river is a value equal to the depth you want to dredge (eg 1 meter, etc)
assign the non-river areas a value of 0.
take your dem and subtract the above ( eg Minus (Spatial Analyst)—ArcGIS Pro | Documentation or other approaches)
you now have a dem with a river whose is deeper.
I have assumed in the above that you dem extends under the river surface with elevation values...!
If not, then the process will be totally different
... sort of retired...
