Do-able.
The HK Immig website would no doubt have the up to date details, but it's relatively easy, just not that quick.
Historically, over a number of years, they would grant you a number of permanent resident visas. Each one valid for a gradually increasing number of years, i.e., 1,2,2,3 etc, and then once you had completed 7 years, you could apply for Permanent Resident.
That gave you a different HK ID card with permanent resident status.
But without Chinese ethnic heritage, your card would not have the 3 stars that showed you were a real permanent resident.
As such the pseudo permanent HK ID card needed to be used for entry exit into HK every so often to keep it valid. I'm not sure of the period, someone on here may know if it's once every 2,5 yrs etc.
The main hurdle used to be finding a sponsor/employer for the initial visa.