Using 3 tricks you can get to the Spirit Temple as early as first leaving Kokiri Forest.
Gerudo Valley Cucco Jump Edit
Discovered by Kazooie
In Gerudo Valley grab the cucco and go to the gate the gerudo is in front of. To the right and left there are small stakes coming out of the bridge. Get on the left one and get on the very edge of it. Now turn around without moving and look at the gerudo. Position yourself so that the left wing of the cucco meets up with the right of the gerudo. Now press forward on the control stick and then right before jumping off hit left. You should get a full jump towards the middle-left of the gate. Right before you hit the gate press B to jumpslash. If you did it right you should get on the fence or hand onto it on the other side. You're not done yet though, be careful to avoid the guards, they can still catch you an throw you into the river. Then just go to the fortress.
Fortress Gate Skip Edit
In the fortress there is a large wooden gate blocking the path to the Haunted Wasteland. Thankfully there is a very easy way around it. Climb the ladder near the gate then at the top turn around and use C up to change your angle to about 45 degrees right. From there simply sidehop left and you will land on the wall to the left that is normally unreachable. From there just move left along the wall until you get past the gate then sidehop back in bounds behind the gate and go to the wasteland.
Crossing the Haunted Wasteland Edit
The first thing you'll encounter is the river of sand. go to the far left and backwalk over it at the edge and you should be able to make it. When you get to the top immediately stop or sidehop so you don't end up going into the "Death Zone". From there just follow the flag poles until you get to the shelter. You probably won't have the Lens od Truth at this point so you'll have to memorize the rest of the path or try following the below video.
Then just get through the Desert Colossus without getting killed and enter the Spirit Temple. By leaving you can get the Requiem of Spirit so you can get back quickly as adult (and cause a time paradox by meeting Shiek as child). Inside you can get early bombchus and Silver Gauntlets which can help you skip Saria's Song and Goron Braclet.