[Back to the Future] If Time Travel is possible, could other people also invent it?

If Time Machine made by Doc Brown was destroyed and he left with the train time machine, could other people later on, invent other time machines in the future with more advanced technology?

Could there even be a type of cold war between different nations trying to gain control of time travel or an international type of police force?

If so, could other future people meet with Doc and Morty and create alternate time lines?