How was gold first discovered in the transcontinental railroad?

I think your question means how did the discovery of gold contribute to the creation of the transcontinental railroad.  There had been some movements toward westward settlement in the 1840s, but that trend accelerated dramatically with the discovery of gold in California.  James Marshall's finding of gold at Sutter's Mill in California in 1848 led to a "gold rush" in the decade that followed, with 1849 seeing a huge influx of people to California.  (Thus we refer to the '49ers.)  The swift settlement of California added incentive to build a transcontinental railway.  The Pacific Railroad Act of 1862 established the charter for doing that.  The First Transcontinental Railroad was completed in 1869.