In truth, laissez-faire is not as connected to the development of the west as people think. The development of the west was brought about largely by the railroads. The railroads were lavishly funded by taxpayer money. This is not laissez-faire.
However, it might be more accurate to say that the development of the west is connected to laissez-faire. Beginning with Frederick Jackson Turner, Americans have held to the idea that the west was developed by individualistic pioneers. These were people who had no need of government help. Because this idea took root so firmly in our consciousness, it came to help justify and promote the idea of laissez-faire. If the pioneers could make it without government help, so should everyone else. This is the true connection between laissez-faire and the development of the west.