Under the Gauss Markov Assumptions - How do we know the Variance is Always Non-Zero?

Question

White's test for heteroscedasticity we run an auxiliary regression on the regressions squared residuals:

$$ \hat u_t^2 = \alpha_1 + \alpha_2 x_{2t} + \alpha_3 x_{3t} + \alpha_4 x_{2t}^2 + \alpha_5 x_{3t}^2 + \alpha_6 x_{2t} x_{3t} + v_t $$

where $ v_t $ is normally distributed. We clearly are looking for a relationship between the error variance and any known variables relevant to the model.

The auxiliary regression always includes a constant term, even if the original regression did not. This is a result of the fact that $ \hat u_t^2 $ will always have a non-zero mean, even if $ \hat u_t $ has a zero mean.

Why is this the case?