private static boolean isValidDate(String date) {
    try {
        LocalDate.parse(
            date,
            DateTimeFormatter
                .ofPattern("uuuu-MM-dd")
                .withResolverStyle(ResolverStyle.STRICT)
        );
        return true;
    } catch (Exception e) {
        return false;
    }
}

Ví dụ sử dụng:

System.out.println(isValidDate("2022-02-28")); // true
System.out.println(isValidDate("2022-02-31")); // false