Non-EU means it's harder to get a permit, especially without working experience, but it's not impossible either.
Housing is difficult in cities like Zurich but calling it impossible is stretching it, especially if one is fine with a longer commute.
Meanwhile the parlement and the anti+immigration far-right vote all the time to increase landlord rights and margins. Most of them are landlords, of course...
Let’s be realistic and admit that landlords already prioritize someone with history of renting in the country and it’s pretty fair to say that new immigrants will struggle to get housing. Even if you come on a FAANG salary, you will not be able to buy your way in that easily.