Unfortunately the only way to upgrade an international itinerary that's already booked is with miles. Mileage upgrades on Int'l trips (Europe/Asia) are only valid on Y or B fares. Since you have 0 miles in your account, you'd probably have to buy some miles to make this work.

I've heard of sometimes being able to purchase upgrades at the gate or at online check in/kiosk, but I've not really ever seen this much.

You could always rebook the itinerary in J (Business). Hope this helps.

As far as Domestic, Platinum upgrades are unlimited and processed automatically, officially 5 days out from departure (although sometimes it happens a bit earlier, like 6 or 7 days out). Sometimes when you buy a full fare economy ticket, the upgrade is processed right after ticketing. When you don't (rarely) get upgraded, you are awarded 1000 miles because of the platinum upgrade guarantee. And also if you have a companion (1) booked in the same reservation, you will both be upgraded at the 5 day window assuming there is space available.