Classic burglar. He is a burglar, not a hit man. He was carrying tools to burglarize a building, not to kill someone. The SWAT costume is an interesting novelty, but its just a disguise. He knew there would be security cameras, so he needed a disguise. He has probably done this before. He seems to have experience. The church was an easy target. Its a big building easily visible from the road, but nobody around at night time. Only one homeowner, across the road, who would normally be sleeping at that time of the night, and would probably be too far away to see what was happening anyway.
He probably arrived about and hour before and hid his vehicle (possibly a motorcycle). He probably broke the window, then hid, to see if the cops would arrive. When no one came, he climbed inside and started breaking open doors, looking for something to steal.
Then the unexpected happened. The woman showed up to prepare for her gladiator class at 4:20AM. He wasnt prepared for that. There was a struggle, and he killed her. Then he took off.
If he messed up and left any clues, he will get caught. But thats not likely, since he seems to have some experience with this.