You've got your work cut out for you.
"The longest knitted scarf measures 4,565.46 m (14,978 ft 6.16 in) long and was achieved by Helge Johansen (Norway), in Oslo, Norway, on 12 November 2013."

Maybe the quickest method would be to destroy other long scarves so that yours is the longest by default, rather than knit one that's longer than 4.5km.
( Aardvark and so at last, I understood, Mon 30 Sep 2024, 14:56, archived)

I know the current record
I made a half-arsed attempt at it many years ago, gave up at 72ft because I ran out of wool
( Smash Monkey 2 The damp spastic, Mon 30 Sep 2024, 15:29, archived)

That's not half-arsed, that's 0.0048-arsed.

( Aardvark and so at last, I understood, Mon 30 Sep 2024, 15:37, archived)

what did you do with a 72ft long scarf?

(sticklebricks it's you daddy!, Mon 30 Sep 2024, 16:20, archived)

Unravelled it
And made blankets with the wool
( Smash Monkey 2 The damp spastic, Mon 30 Sep 2024, 16:32, archived)

👍

(sticklebricks it's you daddy!, Mon 30 Sep 2024, 16:55, archived)