Air Carrier Captain reported a ground conflict critical with another aircraft during taxi out.

Narrative

Pushed off of gate XX and was waiting at spot XX. After getting through to ground on a very congested frequency; Ground told us 'Left on Alpha; Hold short Echo.' My First Officer (FO) read back the clearance. We cleared left and right and I turned on the taxi light and started our taxi. As I continued the turn I suddenly saw a Aircraft Y start to turn towards me from B-M-A; I had to stop immediately and aggressively. I don't believe Aircraft Y even saw me and they were taxing way to fast in my opinion. Also; ATC never mention anything about giving way to another aircraft. This happened fast enough that by the time I stopped my FO never even saw the Aircraft Y until I was stopped.I'm not sure on the cause if this. LGA Ground was extremely busy and in the middle of a departure runway change from Runway 4 to Runway 13. I am really confident we did not miss anything but I can't say the same about Aircraft Y. Keep your head up taxing and be very vigilant about in the Ramp to ground transition.