Yes, many species of birds fly at night. Should we fly at night in their airspace is another question.
What was your IAS? Were you limited by speed control on the SID?
Have your engineers recovered any feathers or other remains to do a DNA analysis? It may help to know what you hit ( or what hit you)
There's a formula about mass times speed etc. so the damge a small bird can do is out of all proportion to its size.
Look at the damage that small bird called Katie Price is doing
Sir George Cayley