As far as we know the universe is infinite, so anything moving any speed will be miniscule in comparison.

What you're thinking of is probably the observable universe, which itself is defined by the speed of light. You can only see light that has had enough time to travel from its source to your eye.

This means what you think of as the universe is defined as speed of light * the age of the universe. If that were the only factors it would always take you the lifetime of the universe to reach the edge of the observable universe while traveling the speed of light.

However the universe is also expanding, the universe is constantly moving away from you, faster then the speed of light for things far enough away. Because of that the universe is much bigger than just the speed of light times the age of the universe, it's roughly the speed of light * the age of the universe * the rate of expansion, so big that you will never be able to reach all that you can see (as far we understand).

It's kind of like asking why a second is so short in comparison to your entire life. Your life is constantly getting one second longer for every second that passes, but at the beginning there was a point where one second was your entire life. Not accounting for expansion, the radius of the observable universe gets one light second bigger every second, but at one point the "observable" universe was only one light second across.