What is the voltage across the capacitor at t=infiniti in this circuit?
Remember that infinity is not a number. So, as \$\small t\rightarrow \infty\$ all the transients can be considered dissipated, and all that remain are the steady-state signals - in this case, a sinusoid.

The capacitor can certainly not be considered an open circuit at large values of time. It will always be subject to a sinusoidal forcing function.

A steady-state frequency response analysis (\$\small s\rightarrow j\omega\$, for example) will give the voltage across the capacitor for \$\small t\rightarrow \infty\$.