I tried IMG yesterday, but it only let me put in a start date of the following day. It's fine if the coverage starts then, but I don't want it to be invalidated if the trip started already.
That's universal. Insurance can only start the day after purchase.
As long as it's medical only, they allow it. GeoBlue don't allow it after trip started. MondialCare allows it even though it's a trip coverage.