With this mission how do you stop the slow motion bit at the start?

you can hit the #2 (switch weapons button) to make the slow-motion disappear. I would recommend joining the public discord server (https://discordapp.com/invite/fQaYqvF) to ask more questions so we can help you easily.

I just tried that but when I watch videos of people doing they cancel the slow motion way quicker for some reason so they automatically have an advantage.

Shooting and reloading immediately also works

I tried that I look at yours and yours is still faster