B757 Captain reported ATC issued last second hold short instructions during their taxi due to a B777 taxiing through the same intersection; resulting in a critical ground conflict.

Narrative

We were taxiing outbound from ZZZ to Runway XR; performing a reduced engine taxi. Our initial taxi clearance from ZZZ Ground was non-standard and we were told to taxi via [Taxiway] 1 and hold short of [Taxiway] 2; exiting from ramp spot X. As we rounded the corner approaching Taxiway 3 we were given last second instructions to hold short of Taxiway 3 give way to a company 777 that was cleared to cross [Runway] XXL after landing on XXR. I attempted to stop quickly; but safely as the flight attendants were performing their before takeoff duties and could be heard moving around in the galley. We were not fully clear of Taxiway 3 as when the instruction to give way was given we were already almost in the intersection. We attempted to notify Ground Control of this but the transmission was either blocked or not acknowledged. All three of us (including our Jumpseater) had concerns with the clearance between the 777's right wingtip; and the top of our flight deck. The 777 wingtip cleared our flight deck by an estimated 5 feet or possibly even less. I felt as if I had reached out the front; I could have grabbed the wingtip of the 777. Without trying to exaggerate; the wingtip clearance between the 777 and us was unacceptably close; and unsafe. We attempted to notify Ground multiple times of our concerns but were unable to transmit effectively as the frequency was extremely congested. We did notice (what appeared to be) a jumpseater in the flight deck attempting to see the 777 wing to verify clearance but I'm not sure if the wing can be seen from the flight deck on a 777; I know on our fleet you can only see the wing from the flight deck if you open the window and look out from there. Even then; it's not an accurate way to judge clearance.I am writing this report NOT to throw the other crew under the bus"; but to document how extremely close their wingtip came to our flight deck; and hope it can be used as an example to all of our crews to SLOW DOWN; be careful; and not push the limit. Just because a clearance has been given; does not mean that you are actually going to clear other aircraft and obstacles. To the credit of the other Captain's understanding of his aircraft's geometry; they did not hit us; but I don't know if this was out of sheer luck or true understanding of his aircraft footprint on the taxiway. All it takes is having your seat out of proper position by a few inches; to result in improper wingtip references by many feet in a large aircraft."