Comma for, e.g., "To the best of our knowledge, ..." and "To achieve this, ..."

If it is not in the style manual, then it is generally preference; however, I tend to defer to adding the comma in this situation.

A short sentence, like the example provided, the comma will not change the meaning of the sentence one way or another. Longer sentences, the comma could change the meaning - where you draw the line...? That can be difficult to say; hence, my preference for using the comma.

Also, I see the comma as guidance for how the author wishes the sentence to be read - i.e., it reflects how the sentence is to be read as though it were spoken. That isn't necessarily applicable in this situation, but a general rule I find to be helpful when deciding to use a comma or not.

A lot of this aspect of punctuation is mandated by usage and not style guides. When you look on corpora sites such as BNC you find that the absence of a comma is unusual in this particular case, and so the example you saw was fairly typical.

Take the second sentence above: after 'BNC', I did not use a comma. I wondered whether I was unusual in this, but a quick glance on BNC told me after this particular subordinating construction we are less likely to see commas. So I've at least got the crowd (people who write for newspapers, which are edited and proofread) behind me!

If you want to know more and see the examples used by linguists, I'd also do a search for 'discourse marker' and 'comment clause.