Translation:Nobody believes that she has arrived by train.
But the first 'person' that was mentioned is "nessuno". How can I know who is meant with "sia"? I would have thought that the sentence translates to "Nobody believes that he/she (referring to nessuno here) have arrived by train." or "Nobody believes that I have arrived by train."
The sentence with omitted parts is "nessuno crede che (io/tu/lei) sia arrivata in treno"
Sia is the same for 1st, 2nd and 3rd person singular but when is 2nd person generally "tu" is not omitted. So in this sentence both 1st and 3rd make sense depending on the context.
In conclusion this sentence is Principal sentence "nobody (subject) believes"
"Che" introduces subordinate
"(Io/lei, subject of the subordinate) sia arrivata (-a because I/she is a woman) in treno