07/27/2011 AT 04:40 PM EDT
The very private Evangeline Lilly
hasn't revealed the name of her baby, but she did give the world a first look at her infant son Tuesday.
The actress, 31, and her little man were snapped after flying into Vancouver International Airport with her boyfriend, Norman Kali.
Lilly's next big project is starring opposite Hugh Jackman
in Real Steel
, which hits theaters in November.