I also think that Link's first step into Termina is when he lands on that Deku Flower after the long drop through the pit.

Still, all the 'rooms' between there and the Clock Tower are very mysterious. For one thing, they all have seemingly bottomless pits...and then there's the twisting corridor, very alike to OoT's Forest Temple. The giant, seemingly metal door that blocks you from getting back into this area later on is also quite odd.

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"Your sword was stolen? That's terrible!"