The phrase "a while to acknowledge" is correct and usable in written English.
It can be used when referring to the time it takes for someone to recognize or accept something.
Example: "It took me a while to acknowledge the impact of my actions on others."
Alternatives: "some time to recognize" or "a moment to accept".
It took me a while to acknowledge this as it was a fairly slow change.
It took him a while to acknowledge that there could be such a thing as journalists who were idealistic and incorruptible".
He took a while to acknowledge cheers from the crowd.
It took me a while to acknowledge the fact that UW Madison's rejection turned out to be in my best interest.
Lanky team captain JP O'Connor, a star on the circuit, is Mikayla's inspiration and also the object of her first feelings of love, though it takes her a while to acknowledge this — to the camera, not JP, yet still no easy thing in an atmosphere of religious gospel and premarital abstinence.
Surely, as the European Parliament, we too must be able once in a while to acknowledge positive results - so that when the people outside hear us, they will see that progress is being made - instead of always using the same negative yardstick.
Writing and performing allowed him a way out, even if it has taken him a long while to acknowledge that fact.
When Google finally copped to the bug, Frederic noted that it took the company quite a while to even officially acknowledge that the easily verified bug existed, but roughly two weeks from bug identification to pushing out a fix actually isn't that bad of a timeline at all.
The regime and state media have little credibility, having waged an unprecedented war of disinformation while refusing to acknowledge a role in the crackdown, blaming the escalating violence on armed gangs and extremist insurgents.
He accepted Scott's decision to abandon the dogs on the Beardmore Glacier, saying they couldn't pull uphill, and he made a virtue of manhauling, while failing to acknowledge that Amundsen's dogs pulled the Norwegians all the way up on to the Antarctic ice-cap far more quickly.
OpenStreetMap, you may recall, is used by Apple for location data for iPhoto for iPhone — something it took a while for Apple to acknowledge.
