There is actually a regulation requiring asylum seekers to apply for asylum in the first country of the EU they reach:
Wikipedia:
”Asylum shopping is the practice by asylum seekers of applying for asylum in several states or seeking to apply in a particular state after transiting other states.[1] The phrase is used mostly in the context of the European Union and the Schengen Area, but has also been used by the Federal Court of Canada.[2]
One of the objectives of Police and Judicial Co-operation in Criminal Matters is to prevent asylum shopping.[3] The Dublin Convention covering the European Union stipulates that asylum seekers are returned to the country where their entry into the union was first recorded, and where they were first fingerprinted. Another objective of this policy is to prevent asylum seekers in orbit, i.e., to prevent the continual transfer of asylum seekers between countries trying to get others to accept them.[4][5]
To avoid abuses, European law, the Dublin Regulation, requires that asylum seekers have their asylum claim registered in the first country they arrive in,[6] and that the decision of the first EU country they apply in is the final decision in all EU countries. However, among some asylum seekers, fingerprinting and registration is vehemently resisted in countries that are not asylum-seeker friendly. For example, some people seek to apply for asylum in Germany and Sweden where a more serious approach to welfare and integration support is taken,[7] and fundamental rights are more likely to be met.[8]
Some asylum seekers report burning their fingers so they can evade the fingerprint record control in Italy and apply for asylum in a country of their choice.[9] The fingerprint record, known as the Eurodac system, is used to intercept false or multiple asylum claims.[10] In Ireland, two-thirds of failed asylum seekers were found to be already known to the British border authorities, a third of the time under a different nationality, such as Tanzanians claiming to be fleeing persecution in Somalia.”