In research paradigm's post-positivism can I prove the hypothesis instead of falsifying it?
In short, post-positivism takes the stance that answers will change with more data and therefore prefers to reject standing assumptions rather than accepting alternatives. Instead of accepting your can say failed to reject. This leaves it in the realm of tentative working belief until more data is presented. 

In length, if you are viewing the world through the lens of post-positivism then you believe that though there is a Reality out there it is not perfectly knowable. An example of this is in the moment of this writing there were an exact number of grains of sand within a given radius of the center of the planet. The quantity however is unknowable. Though it is unknowable we can easily reject the hypothesis that there were exactly ten grains of sand within a thousand kilometers of the earth's center. We have rejected a hypothesis without accepting any alternative. Let us say that an alternative hypothesis was put forward that there were 1 * 10 ^ 15 grains of sand. This alternative though certainly not accurate is much less easy to dismiss. Though I imagine a few quick calculations would be sufficient to reject it as well. We allow to stand a hypothesis that we can not bring enough evidence against to reject but we do not ever say that it is the final and true answer.