While I don't find any requirements on how timely the source distribution must be upon request, one can reasonably say that there must be a line between 1 nanosecond and 1 century.
Courts would most definitely make a distinction here. For instance, one century would mean "refusing to release the source code".
We should test how long it takes Google to release source code upon request. And whether it is 100%. I think we should test whether Google fulfils the GPL here. That's now a challenge.
Google can trivially provide it nearly instantly with no hardship. In fact, it's much harder for them to implement manual handling than automation. They have no justification for it beyond deliberately making it harder. It does have to be provided in a reasonable time or the license wouldn't work. What amount of time is reasonable is up to a court.
Google being incapable of timely handling of these requests is not believable. They're one of the largest tech companies in the world. They deliberately moved from a system without any need for manual handling of requests to requiring it with the clear goal of creating a hassle. By failing to provide it for long enough periods of time to cause tangible harm to people relying on it, they're failing to comply with the license.