It is possible to escape the forest before beating the Deku Tree using a number of different methods.
Requires: Kokiri Sword or Deku Stick
Skips: Deku Shield, Fairy Ocarina
This method allows you to escape the forest by "cutscene" diving off of Navi's dialog into the shortcut to Zora's River without needing the Silver Scale or better. The downside is that if you fail you essentially have to reset the console to try again since Navi will not appear again for approximately 19.5 minutes.
Go through the Lost Woods to the small pond where you can enter Zora's River. Roll from the bank of the pond and grab the top of the gray box. Wait for the Navi icon to appear. You can time this to correspond with the Lost Woods music like in the video. Now press B twice--once to pull Link back off the box, then a second time to jumpslash--then immediately talk to Navi in order to dive off the text as your second jumpslash pulls you back off the ledge.
This method avoids waiting for Navi to appear by clipping into the stone box, but is a little harder to perform.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Obtains: Fairy Ocarina
NOTE! This particular method will require a different setup once you obtain Zelda's Lullaby, as the Kokiri Child's position changes slightly.
Sometimes referred to as "Pokey Escape", this method allows you to clip past the Kokiri Child blocking normal exit. First, head over to right side of the Kokiri Child, and cut down the sign next to him. Crouch down almost parallel to the wall and aim your shield a tad bit to the left. You can also go into first person mode and aim a bit to the left. Typically the jewel of the sword is aligned to one of the green streaks on the wall. Now crouch stab and then quickly press A to clip into the guard. You will want to get ISG.
This will put you within the center of the circle that the Kokiri Child blocks. To get through to the exit from here, you have two options. You can move to a spot within the circle where he no longer says "Speak" on the action icon, and perform a roll slightly to one side, causing you to roll underneath him and escape. You can also 'kill' him by slowly walking to the left side of the log; he will clip through the wall and fall out of bounds, allowing you to walk to the exit.
Requires: Deku Nuts
Skips: Kokiri Sword, Deku Shield
Obtains: Fairy Ocarina
While this method is possibly the slowest (since you must obtain the Fairy Ocarina), it is notable as it is the only escape that allows you to skip the Kokiri Sword, Deku Stick and Deku Shield, making it useful for puzzle or challenge runs.
To perform this trick, start by doing the Walking While Talking glitch, using the crawl space near the training area where you get the Kokiri Sword. After exiting the crawl space, quickly read the nearby sign before the camera focus returns to Link. As an alternative, you can instead wait until Navi wants to talk before entering the crawlspace, then after exiting the crawlspace use C-up to talk. Immediately toss a Deku Nut, once the dialog message box pops up.
You should now have a free range of motion, but it will be difficult to get your bearings as the camera will be locked in place. Link will act as if he's targeting an object where you were originally standing, moving in a circular fashion around this spot.
Navigate Link over to the exit guarded by the Kokiri by finding your way through the fence. You can either zig and zag out of the fenced area, or try to jump up on it and get outside of it from the side. Pay attention to the audio, as Link may grab on to a ledge on your way out.
Once you reach the exit, Link will simply leave the forest. The Kokiri kid will not be there as long as the camera is focused near the crawlspace.
Requires: Kokiri Sword or Deku Stick
Skips: Deku Shield
Obtains: Fairy Ocarina
At the small pond in Kokiri with the waterfall, jump onto the middle platform. Face toward where Mido should be and sidehop off toward the waterfall and jumpslash. If you timed it correctly you should ricochet off the platform and splash into the water. Now activate an ESS by holding your joystick slightly up-right. Make sure you keep your joystick in that position! Now ESS over to where the Kokiri guy blocking your way to Hyrule Field and ESS into the corner that's closest to the Kokiri Sword area. If you have enough speed, when you talk to the Kokiri you should glitch through him. When you finish the text, you should now be a bit inside the tunnel. Now just follow the instruction above on getting out of his circle.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
This was the original method of escaping the forest. First, head to the Business Scrub in the Lost Woods. Activate ISG off the Gossip Stone, and then align slightly to the left. The goal is to sidehop to the left and use the Business Scrub's deku nut attacks to hover in the air. You need to continue doing this along the left side of the wall. After gaining enough height and distance, you must then use the deku nut attack and Megaflip to the Lost Woods bridge.
It is possible to get the same height and distance as in above, but with fewer nuts. This involves using 3 backflips along the wall, this time angled slightly to the right. After the 3 backflips, you now can Z target the Business Scrub and change your angle, just be careful not to get hit from his deku nuts, or shield them back, killing him. You can roll as they are approaching to usually just break them. You want to change your angle to the same as it was in method one, slightly to the left. At this point, you may need one or two sidehops to the left to gain the last bit of height or distance. Then just megaflip like before to land on the ropes.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
The fastest way to the Lost Woods bridge is by clipping through it. This means that the height and distance required are significantly lower. It is an extremely precise trick, but is still possible on a console. You want to aim a little further to the left before starting this one. Only two or three sidehops to the left are needed in this case. Then, instead of doing a megaflip, you can do a mega sidehop. You want to aim slightly to the right of the tree. Link will actually clip the bridge from underneath. The position is absolutely key so watch the video and try and replicate it as much as possible.
Requires: Kokiri Sword or Deku Stick, Deku Shield.
Skips: Fairy Ocarina
Megaflip straight backwards after a sideroll rather than diagonally, then target the scrub and unsheathe a weapon at the right time to get a boost and clip from under the bridge. Because of the extreme precision necessary to perform this trick, it is considered TAS-Only.
1) Take out a deku stick and position as shown.
2) Backwalk off the ledge and backflip in midair.
3) A few frames after you hit the top of the wooden exit, sidehop to the right and continue holding right until you clip through the wall.
4) When oob, buffer to the frame where the diagonal corner of the exit is just before the rupee counter. Buffer a left sidehop at this frame. The kokiri guard will fall out of bounds at this point.
5) Jumpslash back in bounds a few frames later.