Applied via the website. After two weeks of silence, I emailed the recruiter and was invited for an interview after another 2 weeks.

Had two personal interviews with managers/group leaders. After about a month, I received a call from the recruiter with a brief explanation as to why they did not want to proceed.

Prepare a solid list of questions. I was asking questions myself throughout the entire first conversation. Prepare yourself well to talk about ASML's core business; they want you to understand the domain and the basic processes of how their machines work.