Is it possible to convert the given PSD profile into time domain data?
Theoretically possible, this is called Synthesis process, mostly this is dealt by Signal processing engineers. There is no ready-made procedure available for this either in Ansys Mechanical or MAPDL, though one can write an APDL macro for the math, but it becomes involved. However; Ansys nCode Design Life product can do this, attached PSD to Time_nCode Worked Example.pdf give you an idea.