LE had killer DNA from the crime scene
If they used genetic genealogy techniques and a database and found ’match’ that isn‘t a match to a person- it is a match to a genetic line of people which could include thousands
This, his residence location, his car, and his study in school could have supported a warrant to follow him and collect his DNA from trash
BCK DNA then was run in comparison with DNA of killer from the crime scene = 100% match
JMO
It was not only DNA match to a genetic line they followed. LE were tipped about the car, too. And this excelerated the search significantly.
Lets see the time line, I think it will help to understand what happened and how they got him.
Some dates are not precise, there is an element of guess based on information available at this moment
On 13th of November victims were found killed.
13-15 Nov DNA samples taken from the crime scene and sent to lab for testing;
Around 1st of Dec lab tests starting coming back, we do not know in what order,
let's say around 6-7 of December unidentified DNAs (presumably there were more than 1 unidentified DNA) from the crime scene were detected; delayed reporting because they had to test them more than once before deciding there are no match with victims nor to anyone from their inner circle.
7th Dec - first appeal for the white car
16th Dec BK and his Father arrived at PA and took the car for servicing, confirmed by the mechanic at the garage;
Now, let do some maths in reverse order:
Trip from WA to PA - 2500 miles - took circa 3 days.
So, it is safe to assume that the father and son departed from Pullman on 13th of Dec.
We know that LE/FBI were following them during the trip, meaning that BK was already a POI prior embarking on the trip.
So, it is safe to assume that between 8th of Dec ( the day after the first appeal about white car) and 12th of Dec (BK becomes POI) LE received a tip about BK car and checked where the car was registered, who was the owner, verified this is similar to the car they have been looking for from images and video taken by various cameras en-route to 1122; jmoo that LE had at least a part of numbers/letters of the regisration plate of the car and that part matched the BK car plate.
So, on or around 12th of December BK was already a POI.
Whilst FBI was following BK to his trip to PA, LE excelerated genealogy DNA darabase checks, but as they had the surname of their suspect, the search by surname was much faster, as Kohberger is not very common surname.
They selected all Kohbergers from the database and, most likely than not, ooked also for car registration address match, which may narrowed the searched results even further,
Extracted few database records from genealogy DB in a matter of few days to find the DNA match with KB relative.
So, this explains why DNA match to KB relative was found relatively quickly.
I am sure they also checked other unidentified DNAs from the crime scene, to eliminate any errors, which took few more days as they did not have surnames.
I would say, around 23rd of December LE was confident BK is their man.