How long does it take for a sedimentary rock turn into a metamorphic rock?

Could be fairly swift if the metamorphic rock is close to melting and close to an erupting volcanic pipe that leads to the surface where the molten material would solidify quickly.

it depends on where it forms.

By exposure to heat and/or pressure through depth of burial, directed pressure, or proximity to a magma source. Existing minerals can recrystallize, non-hydrous minerals can replace hydrous minerals,...

2 basic steps Heat and Pressure

The direct route would be for the metamorphic rocks to become exposed at the surface and undergo weathering and erosion. The particles broken loose and transported by those processes could eventually...