Well, first of all, it most likely seems that it is infinite, there is no boundary.
However, you have try and think of the universe without time. Pretty much one second before the big bang. This would be the universe before the start of the fourth dimension, time. According to current theory, the three spatial dimensions on the X, Y, and Z axis preceeded the moment of the big bang. If you think of it like that, there is no boundary and the spatial universe is infinite.
But when you add time to the equation, you can only go back so far and therefore there would be a boundary of time which for all intents and purposes would be nothing like a spatial boundary. It is just beyond our understanding to come up with a mental image of what a time boundary might 'look' like.
Take it for what its worth. Not very long ago they thought the world was flat and that the sun revolved around the Earth. So, this could all be complete nonsense.