There's no "reliable" way to do this, as you're interacting with one or more shippers. After shipping physical product around the world since... 2003... every shipper only gives ballpark windows of when they can complete a delivery. Using Amazon FBA will likely provide fastest delivery times.
If its for sales through Amazon (or even elsewhere) FBAPrep.com is one of the best out there. They can handle importing, preparation (repackaging, barcoding, etc.) and then final shipment. Plus, they know the special requirements of Amazon and other third party marketplaces.