Parameterized odesolve solve block?

I am trying to fit data to a "First Order Plus Dead Time" model. I can optimize the fit by using the solution to the FOPDT equation, but, simply as an intellectual exercise, I would like to also be able to do this using the FOPDT differential equation. I have Python code that can do this (it takes an incredibly long time to run; I would guess that Mathcad would take much more time).

The nub problem of the problem as I see it, is that I think I need an optimization solve block to do the least squares fit which, in turn, then needs to call an odesolve solve block with parameters.

I quickly realized that I don't have a clue as to how to do this, and I haven't found any "parameterized solve block" examples that return odesolve solutions.

Attached are my Prime 6 worksheet, text file of data, and PDF of worksheet.

Many thanks,

Roger Gunwaldsen