This is more reason for the gradual approach. Bringing source control, testing, and separation of dev and prod environments, makes things safer and will speed up work pretty soon by making the people much more comfortable to actually try things.
I've done that progressively over two years as a junior and I'm basically unofficial tech lead now. Managers listen to me and I can plan and influence several projects. I have other goals so I won't become official team lead by choice, but that's probably valuable to OP if he can pull that off.
