"At that time, I knew (that) he was seventeen." ->
"I knew he was seventeen."
These should look fine to you, as they're grammatically correct.
Let's look at the colloquialism 'must have been'. By using 'must have been', the author of the lyric is trying to insert uncertainty.
"he was seventeen" = there's a male, age 17.
"he must have been seventeen" = there's a male, probably age 17.
'about' just further enhances that uncertainty by making it "approximately 17":
"he must have been about seventeen" = there's a male, probably age 17 (approximate).
So putting this together:
"I knew he was 17" = I'm certain he's 17.
"I knew he must have been about 17" = I'm pretty sure that his approximate age was 17.
(Also, take note that it's a song lyric, so some colloquialism may be there for meaning and some for scansion.)