"Your best option is to be one of the last passengers to check your bags.
"Bags will always be loaded front to back on the bag carts because more weight has to be in the forward carts for stability while driving, and if you loaded them back to front you couldn't guarantee that the front cart would be fully loaded.
"So if you check in last, your bags will be in the last bag cart, which will make them the last on the aircraft and the first off the aircraft at your destination. If they are the first off the aircraft, they will most likely be the first on the bag carts, and then the first to be unloaded at baggage claim."
"The best way to ensure your bag gets to you the quickest is to ask the counter agent very nicely if they will let you gate check your bag. The downside of that method is that you will not be able to pack liquids or any other items that cannot go in a carry-on bag as you will need to bring the bag with you through the security checkpoint and to the gate."
— Ramp and gate agent Thomas Lo Sciuto via Quora
Responses have been edited for clarity.