[KyleGoetz]

On a tangential note, I don't know how many people actually think about this, but it's painfully obvious when it gets pointed out: はじめまして is the polite continuative (て) form of はじめる, which is the transitive verb "to begin [something]" (as opposed to the intransitive はじまる, which means "[something] begins").

Furthermore, こんにちは is an alternate pronunciation of 今日は, which could be translated literally as "Today/This day is...?"