Scheduling at least two weeks in advance is typically enough time for an auto transport company to schedule your pick-up. However, if your vehicle is in an out-of-the-way location, then you might want to allow an additional week. In most cases, you can get your vehicle moved in 1-7 days, but it is not a good idea to count on that short of a time frame.
Unlike many industries, your likelihood of getting an ideal pick-up time does not improve with more lead time for the auto transport company. Setting up your auto transport 3 months in advance does not provide an advantage over just two to three weeks. So, as long as it is at least two weeks in advance, any time is a good time to schedule your auto transport.
If you need to get your vehicle shipped in the next day or two, due to an emergency or other urgent need, you are likely to be able to find an auto transport company that can help. If they are not able to get a truck to pick up your vehicle immediately, they can arrange for you to drop off your vehicle at a nearby terminal. Just be aware that you may have to pay a premium for this faster service.