Megaflip then damage boost onto the gate. Note that the guards can see you while you're standing on the gate, so you'll have to time the guards to prevent them from catching you when landing on the gate.
It is possible to do a seam walk up with a cucco and after gaining enough height, you drop down and grab the ledge on the other side, also making this possible to go to Gerudo Fortress early with no items at all. Note that the seam walk itself is very tricky since you can fall down very easily from the seam so it may take sometime to get the hang of this trick.
By getting past the wooden gate as a we're able to reach the Haunted Wasteland early, allowing us to skip the Gerudo Card.
Climb up the ladder at the gate so that you face away from the ladder. Do a megaflip. You should land on the mountain behind you if done correctly. While facing the ladder, start walking up the mountain to your right until you cant walk any further. Face the gates center and turn around 180 degrees, then and do a megaflip. You should end up flying between the crossbar and gate if done correctly.
By sidehopping onto an invisible seam, it is possible to sidehop out of bounds around the fence, and then back in bounds on the other siide.
Go to the upper section of gerudo's fortress and walk up the seam to your right. It is possible to get here as adult by doing a Hookshot Jump over the guard. Follow the edge to your right as you are up there until you can't walk any further without falling down. Turn around 180 degrees and then face slightly to the right. After that perform a megaflip. If done correctly, you should be in the lower section of Gerudo's Fortress while it is unloaded. Now all you have to do is navigate to the desert with the help of the minimap, you'll be able to walk through the gate as it isn't loaded.
Note that you can enter the training grounds as child link by doing this.
It is possible to get over the gate by doing a Hookshot Jump. The most practical way of doing this uses the ladder next to the gate, although with a very precise Hookshot Jump that gets a lot of height, it is possible to clear the gate using the flagpole in front of the gate. To get to the ladder next to the gate without getting caught, you can either Hookshot Jump behind the guard from the flagpole of sidehop behind her from the seam to the right of the gate. To get onto the seam you will need to use the hoverboots from the room above the jail.
To cross the quicksand without longshot or hover boots, just perform a Forward Extended Superslide. It's speed should carry you across the sand without sinking.