Obtaining the Master Sword early has the strange effect of leaving the player unable to enter Goron Mines after Forest Temple. However, accessing the Lanayru Province early and using one of the known techniques to enter Lakebed early to obtain the last Fused Shadow allows the player to skip Goron Mines entirely. Lanayru can be accessed much earlier than intended by entering the province from its south point by clipping through the gate blocking the path.
By sidehopping or dashing, Wolf Link can clip through the center of the gate while it is swinging. The sidehop method is the standard, as the dash method is considered TAS-only.
There are two bulblins guarding the gate that should be dealt with before attempting the trick. Runners usually use a spin attack to knock them to the ground, then perform the skip before the bulblins get the chance to retaliate. Alternatively, one could kill the bulblins as wolf by doing two B-attacks (without dash speed) followed by a quickspin or as human (as some categories approach this gate on Epona) with a quickspin.
Once the bulblins are subdued, position Link slightly to the left of the center of the gate with an angle slightly right of parallel and hold target. Hold control stick left and press B to hit the gate and set it in motion. The gate will sway about four times before coming to a stop. Link can sidehop through the gate at any point during this animation, which lasts long enough for four sidehop attempts. The chance of success is not affected by how vigorously the gate is swinging, so one should prepare to input all four sidehops. Link should clip through within a couple of sidehops if the angle was good.
A common mistake is to input control stick left too early. Make sure that target is properly held before moving the control stick, otherwise the intended left sidehop will turn into a left jump attack. Another common mistake is to set an angle that is too perpendicular to the gate. Note that if a retry is necessary it's a good idea to backwalk before bonking the gate again, otherwise Link will sidehop forward past the center of the gate.
The original method of Eponaless Lanayru gate clip was to bonk into the gate then dash through on the correct frame. This is insanely difficult to pull off RTA as not only is it frame perfect, but the frame can vary and sometimes it isn't possible due to the RNG of the gate swinging.
This method is obsoleted by the wolf method above but was the original method used in speedruns for many years.
If you setup Epona's alignment properly you should either:
After voyaging part-way into the province, you will be warped to the Great Bridge of Hylia by the twilight bulblin cutscene.