You cannot apply for it online, it's necessary to show up in person. Since you are moving to the Netherlands, the usual way to get a BSN would be to register with your new municipality of residence as soon as you settle in the country (it's mandatory anyway). You will automatically get a BSN (and a proof of registration, which you would also need for some formalities).
If you really feel you need to register as a non-resident before moving, you still need to show up at one of 19 municipalities including Amsterdam. The page you found suggest that you don't need an appointment for that.
The information available in Dutch is understandably more comprehensive but you will almost certainly find someone who speaks English and is willing to help you in that language at the municipality.