A regular non-weakly discretely generated P-space

We construct a consistent example of a topological space $Y=X\cup \{\mathrm{\infty }\}$ such that: 1) $Y$ is regular. 2) Every $G_{\delta }$ subset of $Y$ is open. 3) The point $\mathrm{\infty }$ is not isolated, but it is not in the closure of any discrete subset of $X$.