Congrats on your new property !!!
Reconnect with vendor, perhaps equipment can be provided for a fee.
If you are very lucky, and have wonderful new neighbours, they may consider helping you out. (Insert here the need for cookies/beer/pizza, possibly money and grovelling) Problems with this plan are many. Scheduling, willingness, appropriate equipment fit for your storage. They are highly unlikely to loan tractor/skid loader to you, unless you can prove your expertise in operation. (Yeah, new unknown neighbour, please take my $100 K or more tractor to your place and see what damage you can do to it. Sorry I would not loan my tractor to you).
Renting is an option, however very expensive. Pick up and drop off in our area will run you $300 then add the rental fees and insurance. If you do not have the expertise to drive it well, you will be slow to unload. Expect a “standing fee” if unloading takes a long time. LOL, consider the potential damage you may do! That shed door may never shut again after you clip it with the loader. If you can plan several jobs on the property, it might make sense to go this route.
Do you have a plan for delivering hay from storage to feeding location? Is that plan workable in all weather conditions?
I believe you should consider cancelling the order, and purchasing small squares until you have the details worked out.