Hello. I am a US Citizen working for the United Nations in Switzerland and I got married to a Canadian Citizen. Does the time I am living with my Canadian wife in Switzerland count towards my residency requirements to apply for permanent residency since I cannot be stationed to work in Canada yet?
As noted, there's no residency requirement to apply for Canadian permanent residency. There's no problem applying for the status, but I warn, PR status is NOT intended for thsoe who might eventually move to Canada. It might even cause more problems than it's worth to do so - because you probably won't be able to meet the residency obligatiion to keep PR status.
I see you are considering what may be useful for ~15 years down the road. Short form, keep looking into it for the long term, as I guess this is you just looking into it for first time more or less. Your plans may change and you should reconsider when they do.
Shortest form for now: your spouse will be able to sponsor you pretty much at any time, count on it taking six months to a year when you do. Realistically that means best time to start applying is perhaps two years before you'd like to move (to allow a buffer, time to prepare, arrange a place to live, things like that).
If in the interim you and your spouse make some arrangements in Canada (visit often, perhaps invest, some banking, etc), that may help your transition.
Important note: US works very differently wrt international organizations for such things, treating it akin to serving in US diplomatic service/military, etc. I.e. your spouse's ability to get and maintain US residency - if she wishes to - is not at all a mirror of how it works in Canada. Other things like taxes are quite different too.