This is very basic, but I have been stuck here for a while.
Consider an AR(1) model $Y_t = c+\phi Y_{t-1} +\epsilon_t$, where $c$ is a constant. If $\epsilon_t \sim i.i.d. N(0, \sigma^2),$ then $Y_1, \dots, Y_T$ are also Gaussian, where $Y_1$ is the first observation in the sample.
I don't quite understand how we have each single realization of $Y_t$ Gaussian. It seems that the conditional distribution $Y_t|Y_{t-1}$ is Gaussian, but why $Y_t$ is Gaussian unconditionally?