What's the most natural way to show a passage of time between the
prologue and chapter one?
I know this is not the answer you want, but the truth is that there is no most natural way. There are techniques that'll be adequate to the story you are telling, there are ones that'll be inadequate. Your judgement as to which techniques you'll choose and how you'll employ them is what can distinguish you and your story.
But it happens that, in your original post, you made a second, different question. Let's take a closer look.
Here's my question: How can I show how much time has passed between
the prologue and chapter one? Is there some technique I can use that
will seem natural?
Kate S. already gave you a great answer, but I'll expand a bit with some examples.
- Jorge Luis Borges' stories were often described as microscopic romances. They were often gigantic ideas that were quickly condensed into their most important aspects and summarized in one ow two pages. Borges accomplished that by ommiting detail, by writing in "broad strokes." He, often, did not give much time to describing what was accessory to the story, such as physical appearance of certain characters, climate, geographical location, etc. He gave only what was necessary and spared no words.
How can this show passage of time? Well, by this technique the reader is forced into filling the gaps on his/her own.
How can you apply this technique? You could drop the Prologue and mention it's important aspects in a vague way in the first or second paragraph of Chapter 1. Now, let me propose a short thought exercise. Take a look at the first paragraph of Kafka's The Metamorphosis.
As Gregor Samsa awoke one morning from uneasy dreams he found himself
transformed in his bed into a gigantic insect. He was lying on his
hard, as it were armor-plated, back and when he lifted his head a
little he could see his dome-like brown belly divided into stiff
arched segments on top of which the bed quilt could hardly keep in
position and was about to slide off completely. His numerous legs,
which were pitifully thin compared to the rest of his bulk, waved
helplessly before his eyes.
Kafka could have written a Prologue detailing the character's transformation from man to insect. But would that be good? We would have lost one of the most iconic first lines in all history of literature.
- A technique I have employed often is showing the reader an element that has changed, and then the passage of time can be inferred. You can describe the natural scenario where the story happens, and tell how winter turned to summer, how the rose buds showed their intense blood-red and fell when their time came, you can tell of the yound trees planted during childhood and felled by the same hands, now adult and rough and cruel. You can tell about time by describing the eyes of the elders, how they became cloudy and milky with blindness, by the teeth collected and cherished by a mother whose children have moved to faraway lands.
Be creative. (I planned this to be longer, but unfortunately this has extended beyong what I originally planned. I might update at a later date.)