Not everyone is looking to the USA for asylum. In 2016, there was 1 205,300 asylum seekers in Europe, 60 % of them seeking asylum in Germany. The same year, there was more than 85,000 candidates for asylum in France. The US are far behind the UE.
Mexicans, evidently, as other south Americans, seek asylum in the USA, and in Canada (the latter being, proportionally, more generous).