Foreword: I haven't actually seen the movie. Allegedly I'm watching it tonight.
“Anyone fighting them must cross a certain skepticism: how is it that the mob, rather than a government or major corporation, controls time travel? We don't associate mad science with bowler hats and tommyguns. We certainly don't associate them with theoretical physics and R&D.
“To this skepticism, appreciate that whoever time travels first will control it retroactively. History will be changed, and it was.
“What do we associate with mob organizations? Moles. Spies. Inside men. Bribes. Things disappearing off of trucks.
“The mob didn't invent time travel. It had two financial backers, and one covert sleeper, in a Pentagon project out in New Mexico. Or it did, in a timeline we'll never remember. What we record is that they pulled the time machine out of the ether, and always had exclusive access to it, and every scientist who ever had a hunch in the right direction has been missing for time unknown.