I can’t see a transient analysis for calculating the capacitor voltage at t=0.01 sec. Note, the system is not at (sinusoidal) steady state at t=0.01 sec, so \$s\rightarrow j\omega\$ doesn’t apply.

I can’t see a transient analysis for \$\small 0\le t \le 0.01\$ to determine the capacitor voltage at \$\small t=0.01\$. Note, the system is not at (sinusoidal) steady state at \$\small t=0.01 \$, so \$s\rightarrow j\omega\$ doesn’t apply.