Hello,
In direct answer, no, you do not log in first.
In indirect answer, this error message means that your account is ineligible for the event. Unfortunately, activity for this event is based upon the entire account, not just characters on a server. If your account has logged in within the prescribed period (from December 7th onward), then it is not eligible to participate. Judging by the screenshot you took, it looks like your account was active 8 days ago, meaning it was last active on December 17th. Accounts need to have been inactive since December 7th in order to be eligible, so your account does not qualify.
Sorry for the bad news, but keep in mind that you can still participate in this event as a recalling player and get rewards from other returning players.
Thanks and good luck!