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Why did you replace the engine ?
Where did you source the replacement ?
If the previous engine failed what were the circumstances of the failure?
Have you had the cylinder head off or was the new engine sealed and complete ?
White smoke normally indicates oil getting into the exhaust via hot side turbo turbine bearing and oil sealing ring .
Normally if oil is getting into the combustion chamber the smoke will be blue rather than white.
If the previous engine failed in mega fashion then your exhaust pipe , oxy sensor and cat may be filled with engine oil which is burning off . Did the previous engine hole a piston or have a mega turbo failure?
Assuming the short engine you instaled was sound and that the head/ cams etc are not damaged from lack of oil and that you assembled every thing correctly yes it should be ok .
The thing is to get it running safely with out consuming its own oil and smoking . THEN we can safely run the engine for a while to record some fault codes in the self diagnosis system . This will enable us to diagnose the source of the mis fire by reading the codes ....... IF it is still misfiring ......... one thing at a time in priority order is the best route I would respectfully suggest .
We know from your account of the engines demise that the turbo has trashed its bearing from lack of oil . The turbo runs very very hot indeed and a brief period without oil will trash the bearings allowing pressure fed oil inside the turbo to escape directly into the exhaust pipe . This causes the white smoke you have described.
did you notice the condition of the cam lobs and followers and the cam journal bearings in the cylinder head on reassembly .........were they ok ?