There will be no old Toho roars or footage in this film. Gareth said he imagined it "as if" someone from Toho saw his version and went back to the studio to make a film on it. Never did he say that anywhere in his film would he actually make that idea a part of his story. In fact, it'd be rather stupid if he did. Having our real modern Godzilla pop culture in a movie that's a reboot to the franchise and starting something brand new would completely defeat the purpose. That, and it would be a partial break of the 4th wall, so to speak.
Anyway, as for his appearance, you must clarify whether you mean our first encounter with him or his first full body reveal. If you mean our first encounter with him, then it will likely be in the first few minutes to introduce audiences to the fact that there is something out there that is going to be a BIG problem. If you are asking about his first full body reveal, it will likely be during the first major battle of the film, slowly teasing him bit by bit until the reveal is presented.
I doubt very much that they will use any of the old Godzilla entrances in this film. Gareth is a creative man, and his special effects team is the top of the line in America. They should be able to come up with something entirely new and amazing for the Big-G's American debut.