Checkmate in how many????
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with the opponent playing back as best as he can
"As best as he can" really depends on the player's strength. 
If the opponent plays back flawlessly, then it is possible that checkmate cannot be achieved - although it is up to the engines to solve chess, ultimately. At this stage, at least, the amount of calculations required far surpasses anything doable within the next few trillion years with the current technology.
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Does any body know the least amount of moves before checkmate/draw from the beginning position
Can stockfish or any chess engine figure this out?
Which one will do it the fastest?
How much time would it take?