Not necessarily. I think that we can imagine our lives having individual purposes without necessarily implying the existence of any single cosmic purpose.
If we go with the local goal-directed behavior in our lives as opposed to an over-arching cosmic purpose, then the question arises of what drives and steers our motivation.
The Buddhists might derive our propensity to think of our actions and behavior as meaningful from dukkha and desire. They might say that we provide ourselves with our purposes in life by choosing and then pursuing goals that we imagine will finally deliver us the elusive lasting happiness that we seek. (Wealth, power, knowledge, sensual excitement, beauty, love, perhaps even peace and enlightenment...)
Perhaps that man, composed as he is of an ever-changing process taking place among elementary particles, skandhas or dharmas, defines whatever purpose and meaning seems to him to exist in his own life by his choice of goals.
After all, even if God (or the universe) does have a purpose, some transcendental teleological goal that everything is moving towards, that purpose will still be God's and not ours. We might still say -- "Yeah, it's great that God has a purpose in creating all this, but what about ME? What about my life??" (Maybe the universe is just a giant ant-farm that a juvenile God is idly toying with before throwing everything away.) Whatever grand cosmic purpose that might exist still won't be of any use to individual human beings until we can bring it down to our own scale and internalize it somehow in our lives, until we identify with it and make it our own.