I think a useful point of comparison here would be to imagine an untouched snowy landscape. The landscape is clean, white, and unmarked by anybody's footsteps. When you set out on a journey across the snow, you leave your imprint on it, and it will never be the same as it was before. You can also see, if you look, the places where other people have walked: they are going through the same field, but they are traveling on their own journeys, separate to yours.

The blank sheet of paper, then, is like this untouched landscape. It is filled with possibilities. Just as our journey through life is our own to direct and will leave its own mark on whatever we encounter, we can shape other journeys depending on what we write on the piece of paper.

For a writer, a blank sheet of paper can even offer the opportunity to construct a whole universe. It offers us the chance to sketch out the journey of a fictional protagonist, created purely in our imagination. We can decide where this person was born, what his family was like, what career he embarks upon, and what happens to him. The unmarked paper is an invitation to the writer to leave their mark upon it. But as we draw out the journey of a fictional person, we may find that we're leaving footprints in our own broader journey through life, too. This piece of paper can't be unmarked, and our path through life can't be untrodden.

In order to answer this question, one must look at life in metaphorical terms as a blank sheet of paper. When we are born, each and every one of us is about to embark upon a life's journey. Naturally, when we start out on that journey, we have no experience that we can use as raw material for the story of our lives. So our sheet of paper, as it were, is blank when we are born.

As we progress through life, however, we gain more experience, and as we do so, we will find that what was originally a blank sheet of paper has become filled up with experience. In due course, that experience will form the basis of the life story that each one of us will be able to tell.

Even if the journey isn't a particularly interesting or exciting one, it can still form the basis of a life story. What matters here is not so much the content of a story, but the very fact of its existence. In other words, it doesn't really matter what we cover the blank sheet of paper with; the main thing is that it's covered.

And by covering it, we can confirm that we have had many experiences, experiences that may not mean much to anyone else but which have nonetheless shaped the general direction that our life journeys have taken.

John Locke, an Enlightenment philosopher, coined the term tabula rasa, meaning blank slate, to describe the idea that each human being is born without knowledge or ideas. We are blank, so to speak, when we come into the world. We gather information through our five senses, and then we begin to use that information to form ideas and concepts. This is the journey of life. A blank sheet of paper is, literally, a blank slate on which one can write or draw or paint anything! There are endless possibilities: one can write a journey of adventure, some quest that must be fulfilled by a heroic woman or man; one can write a love story, full of courtship and drama and ending happily ever after; one can write a mystery, full of clues and red herrings; one can write about any kind of journey, even an interior journey of maturation or realization! The blank page also encourages the writer to go on a journey of sorts as well, as writing requires a good amount of soul-searching.

I think that the blank piece of paper can be linked to the theme of the journey in a couple of ways.  All journeys begin with the unknown in front of them.  Literally, each journey's start is a canvass where the protagonist who must undertake the voyage has to paint the picture or write the story of that quest.  The blank sheet of paper represents the hero who must confront a journey in front of them, waiting to be taken and waiting to be born.  The paper cannot write itself.  Someone must write the narrative that the paper will hold.  In much the same way, the journey itself cannot be undertaken unless a protagonist is willing and able to assume leadership in the voyage.  

Within the contours of the paper can be hurt and joy, pain and elation, community and isolation.  These narratives can be written on the paper and these narratives are part of the journey.  The blank piece of paper is a symbol of all that is to be written.  It is reflective of everything that can be, the hope and promise intrinsic to endeavor.  In much the same way, the start of a journey contains such hope.  Both feed into what can be as opposed to merely looking at what is.  This would be how the profound meaning of the blank piece of paper is reflective of the journey.