Personally, I say Ideally 3–6 months in advance to secure the best rates and dates. This gives you enough time to compare moving companies, secure better rates, and make sure your preferred dates are available — especially during busy moving seasons like summer.
International moves involve a lot more logistics than domestic ones: customs paperwork, potential shipping delays, and coordinating with destination services. Movers also need time to arrange container space or freight bookings, which can fill up fast depending on the route and time of year.
Booking early also allows you more time to plan around any unexpected changes. Documents might take longer to process, or you might find out you need extra paperwork for your pet or personal items. Giving yourself a wide margin for preparation is one of the best ways to make an international move less stressful.