One of the assassins was tasked to kill both mother and daughter, and he knew just where to find them because of the intel they got from the party. So it was not hard to find them and execute his plan. When he got to the nursery, Mrs. Russo was already asleep on the daybed. As he was trying to suffocate the baby by using a pillow, he heard hurried steps heading his way. So instead of failing his task, he decided he would take the baby instead and do the deed outside. He jumped out of the building and made a run for it.
What he didn't account for was that one of the security guards would hear the baby and see him jump out the window. The guard followed him, shooting him in the leg, which slowed him down. He could have gotten rid of the baby and left it right there in the forest, but he was not going to fail, and have them find her, so he decided he was getting rid of her somewhere else.