Let's suppose you dug out a foot deep in your 25'x25' garden. It'd take 25 pickup loads to haul it. Haul it to where and then shovel it out of the truck. Sounds like about a month long task. Or an expensive job with a Catapiller loader, a triaxle truck, a crew of 4 or 5. You can't haul more than a cu yard of dirt in a pickup, because of the weight.
Or, you could rent a pickup, buy 4 yards of mushroom manure and haul it in two loads. Unload it in one day. It's light, it digs easy with a shovel. You load it into your wheelbarrow, push it to the back and dump it. Dump the next wheelbarrow in a different spot, spread it with a rake and start digging or rototilling it. Or you could hire a crew, get a
mortgage on the house and wait for the crew to show up.
I'm picturing your 25x25' foot garden in NorthEast Philly. I can't imagine that garden space in South or North Philly. There was an apple discovered in West Philly on a corner, but that was in the 1800's. I can't picture it in West Philly either. I'm picturing a small
city yard, the house in 2 or 3 feet higher than the street. I can't picture the back of the yards, it's been too many years. But I can't imagine a triaxle and that loader in that neighborhood. And I don't picture a wealth of dead tree limbs.
You want to plant a garden grow some veggies, maybe some flowers, put in a dwarf
apple tree... maybe. Tomorrow it'll be April, you could have been planting 3, or 4 weeks ago, your already late.
You could look for compost, I've never seen compost sold, it's something you do for your ownself. You don't need to finish the whole garden plot to start planting some seeds. You don't need a major project. You need a spade, a wheelbarrow, a bag of lime and something to improve the soil. You can buy peat, a 3 cu ft bag for $10, that's $90 a cu yard or buy the mushroom manure for $35 a yard, rent a pickup for $19.95 plus the mileage. On Monday evening you could haul a load and Tuesday morning haul another load. Get going, it's getting late in the season.
I'm trying to remember where there are horses in the Philadelphia area. I'm thinking the Main Line. I remember horses in Valley Forge Park, next to the covered bridge, but that was 40 years ago, it's probably a lot of houses by now. But if you can find horses they usually have a big pile that they give away for
free. You'd need to scout it out before you rent the truck.
Good luck with your garden.
edit:
If you have grass where the garden will be, I'd turn over the sod into the clay, you need all the help you can get breaking up that clay. Some say to haul away the sod, that's where the weeds are. I knew someone who hauled all the top soil away, "that's where the weeds are". I ignore those ideas, the better the soil is the more weeds there are, the weeds will grow bigger, but so will the lettuce.