I heard that a magnetic field only creates a force on a moving charge, not a stationary one. However, what if the solenoid containing the magnetic field was moving through a stationary charge. Would that create a similar force? Thanks!
Yes. A changing magnetic field generates a changing electric field, that acts in the charge ($\mathbf F = q\mathbf E$).
Another way to see the same effect is moving to the frame of the solenoid. Now the charge is moving and a magnetic force acts in the charge ($\mathbf F = q\mathbf v \times \mathbf B$)