See Quest Oddities for more information on the effects of obtaining Zelda's Lullaby early.
See Forest Escape for more information.
It is possible to skip Mido (who blocks the entrance to the Deku Tree as a Child, not the exit out of the forest), allowing you to skip obtaining the shield. However it is quite difficult to achieve.
By avoiding the trigger that loads the Deku Tree map, it's possible to enter the Deku Tree as an adult.
Equip the hover boots, and walk over to the root of the tree house to grab the roof. Unequip the hover boots, and angle yourself towards the far off ledge. Turn around and place a bomb behind you, then turn back to face the ledge. As soon as the bomb explodes, use pause buffering to advance to the first frame Link jumps and equip the hover boots. Hold forward on the unpause, and jumpslash just before Link reaches the ledge to gain some extra height and distance. From here, you can navigate your way on the ledge to the unloaded Deku Tree area and enter the dungeon as an adult.
This method is particularly useful if you have just beaten the Forest Temple, as it puts you right next to the Deku Tree.
1. Go to the left side of the Deku Tree where the gossip stone is.
2. Get into the corner where you will clip.
3. Align the left side of the B button to the left side of the gossip stone.
4. Superslide and equip the hover boots, also release the target (Z or L) button.
5. Once you clip into the void let go of the shield button and hold up-right on the control stick to curve your hoverslide towards the load zone. Press B to jumpslash near the end of the hoverslide in order to greatly increase your chance of reaching the load zone.
After preforming the hoverslide, make sure to hold both Z and R and hold right on the control stick. As soon as you clip, let go of R, but continue holding Z and right. As soon as the hoverboots wear off and you here Link gasp, continue to hold the control stick right and press B to jumpslash.
If you do not have the hover boots, it is possible to just hover along the wall where Method 1 is done to also reach the loading zone. Note that this can be made easier with a few chus.
It is possible to do the above method without any explosives. This requires the Forest Temple to not be beaten yet, and use the octorok's attack to hover along the wall. Inverting your camera angle and using the large Deku Baba to get two hovers off of the ground can also be extremely helpful.