A curve can't have a starting point in the middle. It has to be one or other of the end nodes. In Inskcape you can reverse the path direction using Path > Reverse. Path direction affects the entire path. You can't have sections of a compound path running in different directions. Only open paths have a start and end node (see note below).
If you want you can change the preferences to show the path direction. Click Edit > Preferences > Node. Select the option that says "show path direction on outlines".
When you show the path direction by clicking on the path using the Nodes Tool, there are little arrows shown on the path like this example:
Note: A closed path has no start node as such, only a direction. There's no way to indicate a start node in the middle of a closed path, or to have sections of path running in different directions. Path direction affects the entire path. Although there might be a way of editing the SVG XML so that a particular node comes first in the path data - but you'd need to do that manually. As far as I know, there is no way to select a node in a closed path and change it to be the first one by applying some setting in Inkscape. Perhaps there's an extension somewhere (or someone could write one) that could do it, but I haven't found one.