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SAN DIEGO (CBSMiami) – The first group of Central American migrants that trekked across Mexico seeking asylum in the U.S. is being processed.

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Members of the so-called caravan cheered and pumped their fists when news spread that eight women and children were allowed to cross the border. Their entry is a milestone for the group, marking the end of a month-long journey from their home countries.

The caravan’s organizer said “we are happy, celebrating. these are eight families who don’t have to suffer anymore, who have the opportunity to reach a court.”

About 140 are still waiting to enter the U.S., setting up an encampment in Tijuana, Mexico after officials from the U.S. Customs and Border Protection announced that the San Diego port of entry was full. This group has become the focus of the Trump administration – overnight the president tweeted about them.

Those seeking asylum will have to prove a credible fear of persecution in their home country.

“That credible fear interview can take a couple of weeks for an immigration officer to actually see you,” said immigration attorney Carolina Gomez.

If they pass that initial interview, they will likely have to make their case to a judge, who decides whether to grant asylum.

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According to a new asylum tracking system, Los Angeles judges from 2012-2017 heard thousands of cases. Many seeking asylum were denied. One judge heard 400 cases and granted 83 percent asylum in the U.S. Another judge heard over a thousand cases and gave just two percent asylum.