There is data on the subject of the amount of gold brought into the US by immigrants. It was requested by the Treasury Dept and provided by steam ship lines for multiple classes of passengers. First class had a little gold to exchange in Europe and vice versa, but they used letters of credit for most things. Steerage passengers often carried all they had in the world, with most possessions turned into coins and paper currency; most was paper with a few silver and gold coins, but not a large sum -- $5 or $10.
Experiences after landing in America depended on what the immigrant family did for income or by trade. Farmers had almost no cash of any kind except at harvest. Merchants cycles money through the business; wage earners barely paid the bills unless fortunate to have a needed skill.
I feel that most commentators give entirely too much credence to claims that ordinary people used gold coins or to its importance in the economy. Most of the stuff sat in Government vaults -- it was not wanted.