Where does the BJT fall into saturation region as per the output characteristic?

Seems basic, but I fail to see in this diagram how the transistor will fall in the saturation region.
For a given Ib, wouldn't the Ic value just trace the blue line for whatever value of Vce from start zero to Vce max?
Say for about 1 volt Vce and Ib=80, I can trace about 45ma Ic(the blue curve), or should I just follow that green patch on the left and say Ic is near the red bar on top?

Stay on the blue curve.

As noted on the diagram, the saturation region is the area to the left of the blue traces. So, for the given load line, it would be to the left of where the load line intersects the mostly vertical blue line.

The independent variable is base current; the dependent variables are collector voltage and collector current, which are a function of the load resistor...

I had a hard time finding a transistor in my library that has a β as good as the one depicted in your figure... Mine reached saturation at about 160uA.