Initially there is no current flowing through the solenoid, so, no flux was passing through the metal ring. When the current is switched on, the current in the solenoid will be as shown, the flux (downward) increases, and this will cause a counter clockwise current (as seen from the top of the ring) and the flux passing through the ring increases.
According to Lenz’s law, this increase will be resisted, if the flow of current is in the opposite direction to that in the solenoid, so they will repel each other, and the ring will move upward.