If I'm interpreting your question correctly you are asking how to analyze a DOE using historical data.
We all wish to extract as much knowledge as possible out of historical data. I've found that in almost all cases though the historical data was not gathered in a way that facilitated the answering of any project related questions. I believe there is an applicable quote from Tukey regarding this aching desire. I do wish you're more lucky than me though.
You could try to apply multiple regression on that production data, but my fear is it will be failing certain assumptions.
It's unlikely you're Y is a function of a single X. I would instead suggest establishing an experimental objective and then gathering some data to run a sequential experimentation approach. First widen you're options with some structured brainstorming and direct process observation. Once you've gathered more factors besides the one you want to optimize run a fractional factorial to see if they're significant. Are you really sure this single factor tells the whole story? Near optimum the response surface can be complex consisting of multiple factors and possible interactions.
After the fractional helps you identify what factors could be important then start to optimize by applying a steepest ascent approach. Use sequential experiments to hone in towards optimum and when you think you have level settings straddling the optimum run one more and include 5 center points to determine if there's any curvature and check for repeatability. Then add axial points to finish the optimization.
Of course all of this is hypothetical and really depends on your specific situation, the data will guide. As long as you keep it small and sequential you have the option to pivot when results don't match expectations. And since you're running small experiments, you don't waste resources along the way as you surely get surprised and must pivot.
There are many experimental strategies besides this one, but it's my favorite and tends to be relatively straight forward.
Goodluck
