The fastest 1km I ever ran was around 3m20s, I felt like I was sprinting, and was fully cooked at the finish line.
Afterwards I did some quick numbers and realised the average marathon runner was not only going a lot quicker than I was, but they were doing it for a further 41km
You've proven you can run one kilometer. You just need to prove that if you run any km, you could run the next km, then you're done.