You can put any block height there, at any time, it's just text. It's like me sending you a photo of myself as I am right now, only I'm holding a newspaper that was printed 14 years ago, and telling you the photo is 14 years old.
You need some kind of external party/method that allows you to sign your note with the current block height, in a way that isn't falsifiable. A Bitcoin node would probably have to participate. You send your note, a node embeds the block-height somehow or co-signs, something like that, I'm not knowledgeable enough. 😂
Make sense?