Remove cooled cake from baking dish and slice into ¾ to 1-inch cubes. Set aside.
In a large mixing bowl, use a hand mixer to beat together the cream cheese and vanilla extract until smooth.
Beat in the pudding mix until fully combined. The mixture will be thick and lumpy.
Slowly drizzle in 1½ cups of the heavy cream, beating on low constantly and fully incorporating each drizzle of cream (about ⅛ cup at a time) before adding the next drizzle.
When the cream cheese/pudding mixture is smooth and creamy, add ½ cup of powdered sugar and beat until combined.
Add fresh strawberries to the mixture, reserving about 1 cup of the strawberries for the top of the trifle.
Build the trifle by layering ⅓ of the cake cubes, then about ½ of the strawberries and cream mixture, another layer of cake pieces, the remaining strawberry mixture, and then the final cake pieces.
In the bowl of a standing mixer (or you can use a hand mixer), use the whisk attachment to beat the remaining two cups of heavy cream until soft peaks begin to form. Add remaining ¼ cup of powdered sugar and continue beating until the whipped cream forms stiff peaks.
Mound or pipe big dollops of the whipped cream around the top of the trifle. Pile the reserved strawberry slices in the center. Pipe one more dollop of whipped cream in the center and top with a halved strawberry with the stem still attached (or decorate as desired).