Good advice so far. A hand truck with solid tires, not pneumatic, most likely will help a lot. Use a couple of ratchet straps to hold the crates to the hand truck. Have the friends balance it for you, hand trucks are narrow compared to most crates, so tippy! You can also rent appliance moving hand trucks that have built in straps, heavier frames and often stair climber helpers. Much better than the HF hand trucks.
Lift gate delivery usually means they will get it to the ground for you, no further. That means it will likely be on the street in front of your house. LTL service is notoriously rough on shipments, look everything over closely for exterior damage before signing for it. Make notes of any suspected damage on the bill of lading, have the drive sign the notes. If you don't do that you are responsible for any damage.
Get some strong friends, just in case, & a case of their favorite beer & pizza.