I applied for a intern position at a London office (an SV company) not in my home country in December and I did get an invitation for an onsite (travel covered by them) 2 weeks ago. The recruiter mentioned for me to choose some dates within 3-5 weeks and I chose it in the 5th week. The position has been open for application for about 5 months already (closed 1 week ago). Do you think my onsite would be too late then and the position would have been filled before my onsite?
Do you think my onsite would be too late then and the position would have been filled before my onsite?
No. Since you chose a date at the very end of the range presented, I don't think the position will have been filled before your visit. If they needed you to be there before the 5th week, they wouldn't have offered the possibility.
In the future, try to show more enthusiasm by finding a way to jump on such offers as quickly as possible.
For this time, just be prepared to wow them once you are onsite.