You can proceed in a much simpler way. The 3 valid cases are very similar and can be treated as one, the game can be started only once after the loop because we know that once the loop exits, level has a valid value.
boolean valid = false;
int level;
do {
try {
level = scan.nextInt();
valid = 1 <= level && level <= 3;
if (valid) {
System.out.println(String.format("You selected level %d !",level));
} else {
System.out.println("That's not an option!");
}
} catch(InputMismatchException input) {
scan.next();
System.out.println("That's not an option!");
}
} while (!valid);
// start the game