From what I know, the GARCH(p,q) model is estimated via MLE and through an iterative process. Let's say if i wanted to recreate a GARCH(1,1) parameter estimation with excel solver (through maximizing the log-likelihood), how are my initial GARCH terms $ \sigma_t^2$ set?
More specifically, given $ \epsilon_t = v_t\sqrt{\sigma_t^2}$ where $$\sigma_t^2 = \alpha_0 +\alpha_1\epsilon^2_{t-1}+\alpha_2\sigma_{t-1}^2 $$ how does the process of parameter estimation start since we do not know what $\sigma_{t-1}$ is?
One answer I've read from here shows that the program set the initial GARCH term to be the sample variance or its expected value. Is this how we approach it?