I'm not understanding the goal of your question. On a two axis plot, you can set the minimum of the principal y axis with the limits argument of scale_y_continuous and that will set the minimum of the secondary axis through the transformation used in sec_axis(). I guess you want to calculate that minimum on-the-fly. What is the rule or the goal for setting the minimum? That is, what do you want to achieve that the automatic scaling of ggplot does not?
Sorry if I'm being dense.