Welcome to the Cove!
I would approach it like implementing 5S, by starting with an area where the changes would, if possible, recognizably improve people's lives.
You might also ask people what they would like to see you start with. People generally know what's unsafe but maybe are not likely to speak up on their own.
Changes should focus on engineering first, such as installing rails for fall protection and guards to keep people from lopping off their fingers in machinery. Light curtains are effective. After that, use administrative controls such as switching tasks to prevent fatigue and the risk of absent mindedness of rote routine tasks (I lost a finger tip with one of those). Lastly are behaviors, such as inspecting and wearing fall protection harnesses. Lockout tagout is a very important program but it requires much discipline in some applications so expect a learning curve and long term behavior shift.
I hope this helps!