I have the following data:

y x
1275 230
1350 235
1650 250
2000 277
3750 522
4222 545
5018 625
6125 713
6200 735
8150 820
9975 992
12200 1322
12750 1900
13014 2022
13275 2155

I would like to find reasonable initial values for the model

$$y=\alpha+\beta_1\text{exp}(-\beta_2 e^{-\beta_3 x})+\epsilon$$

What I know:

For the Gompertz model, the inflection point satisfies

$$x=\text{log}\left(\frac{\beta_2}{\beta_3}\right)$$

For the Gompertz model with an intercept we have

$$\lim_{x\rightarrow\infty} \alpha+\beta_1\text{exp}(-\beta_2 e^{-\beta_3 x})=\alpha+\beta_1$$

so we can set $\alpha+\beta_1=13275$, the maximum value of $y$ in the dataset.

However, I can't seem to combine what I know to find initial values.

I would like to find reasonable initial values and not rely on specifying an exhaustive grid of values.

Any ideas or suggestions would be appreciated.