Obtaining the Master Sword Early has the strange effect of leaving you unable to enter the Goron Mines after the 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 you to skip the Goron Mines entirely.
By bonking the gate with either a B-Attack or a Jump Attack and then sidehopping into the gate as wolf it is easy to clip through after a few tries. A B-Attack is recommended over a jump attack, to execute this trick have a slight angle away from the gate as shown in the video so when you hold left while targetting you get the action commend to "Jump" which is sidehop, if you jump attack when holding left then you are having got a big enough angle away from the gate. Once you have the angle, hold target and left then press B to B-Attack the gate, after this start mashing A while holding left to sidehop, which a small amount of luck you should clip through. In a run you would either ignore the bokoblins by dashing past them and quickly targetting of kill them with B-Attacks and a spin.
The Original method of Eponaless Lanayru Gate Clip was to bonk into the gate then dash through on the correct frame. This is insanely hard to pull off RTA as it is frame perfect, the frame can vary every time and sometimes might not be possible due to the RNG of the gate swinging.
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.