The player can't win. Analysis to follow.
Here I've marked the "safe" moves in blue. We will call them 1, 2, and 3 counter-clockwise starting from the left. The sacrifices I have marked in green. Let us call them A above and B below. Finally I have marked a move inside the lower right square in red.
First to address the red move.
Any move inside the square is bad:
Assumption - It is determinable whether the first person to make a move outside the square will win or lose.
Making a move inside the square gives the opponent the opportunity to decide who makes the first move outside the square. This is because they can either complete all the boxes in the square then move outside, or continue our line inside the 2x2 square to split it into 2 2x1 squares. In the latter case we are forced to make the first move outside the square (after completing the four boxes). Since our computer opponent is perfect, it will know whether it wants to make the first or second move outside, and will choose accordingly. We cannot give the computer that choice.
Which move to make.
We need to note that 2 is mutually exclusive with each of 1 and 3. Also, A and B are mutually exclusive. Any non-safe, non-sacrifice move will be as bad as the red move. Finally, A has interactions with our three safe moves. If A is played: with 3 on the board, 1 and 2 become starts to long chains (bad), and without 3 on the board 1 and 2 become sacrifices.
Unfortunately, all this combines in a way that appears bad for us.
If we make a move in one of the safe lines, the computer can play A leaving us with no good moves like so:
case 1: 1, A, complete the squares...in doing so we have played 2 and have no more valid moves (2 invalidates 3, and A invalidated B)
case 2: 2, A, complete the squares then no more valid moves (likewise 2 invalidates 3, and A invalidates B)
case 3: 3, A, complete the square then no more valid moves (A invalidates B, and 3 + A means 1 and 2 are starts to long chains)
So what if we start with a sacrifice? The computer can follow with a safe that leaves no good moves.
case A: A, complete the square then 3, no good moves (A invalidates B, and 3 + A means 1 and 2 are starts to long chains)
case B: B, complete the squares then 2, no good moves (B invalidates A, and 2 invalidates 1 and 3)
We're left with no way to win this, but the best move is probably 1 or 2 as that forces the computer to sacrifice 2 squares.