There are two issues with AC, how the steady state works, and how we get to the steady state from from initial zero starting conditions.
You are concerned that current will never flow. Let's look at the starting conditions of no initial current in the inductor. When we connect it to the supply, there will typically be a finite voltage across the terminals. With a voltage across the inductor, we know the current will build, at a rate given by dI/dt = V/L. So now we have a current flowing.
Let's address your ideal circuit. You have a voltage source, with no internal resistance. You have an inductor, with no internal resistance. That means you have a loop with no resistance, so the current is undefined. If you input this circuit into a simulator like SPICE, it would object, some would say 'matrix not invertible', the smarter ones would say 'zero impedance loop'.
The lack of resistance means that the current that started flowing when you first connected the inductor, the initial transient, would continue forever, without dying out. In the real world, there's always resistance (except for superconductors where the initial transient continues forever without dying out).
This means that if you want to solve for current in this particular circuit, you will have the superposition of any everlasting initial transient, and the long term steady state result. This will complicate your mental picture of what's going on.
The easiest way to resolve this is to connect the inductor at a time which gives you no initial transient. Paradoxically, this is at the peak of the AC voltage.
Connect the inductor. AC voltage is at its peak, inductor current is zero. Current starts to build, and continues to build until the input voltage has dropped to zero. As the voltage dips negative, now current starts to fall, and for a nice symmetrical waveform, current reaches zero by the time the voltage waveform is at its negative peak. That's the first half cycle done, run through the same argument swapping the signs for the second half cycle. This is one cycle of the steady state.
There are two ways of interpreting this current change with voltage behaviour that's summed up by the equation dI/dt = V/L. We could say that the current changes because of the applied voltage. We could say that the change in current generates a voltage exactly equal to that applied. Actually what happens is that both things happen at the same time. We cannot meaningfully say that one causes the other, in the way that kicking a ball causes it to move, because the moving ball certainly does not cause the kick, this cause-effect is not reversible.
For resistive inductors, we can switch on at any point in the waveform, and the initial transient will gradually be damped out by the resistance, leaving only the steady state. The higher the resistance, the faster we'll settle to the steady state. It was only in this zero resistance case that we had to start at peak voltage, to start already in the steady state.