If they WANT your DNA then a swab/split is the easiest way.

They could take your DNA along with testing for COVID.

I personally don't see why they actually NEED more DNA samples since so many people have done those ancestry DNA tests voluntarily though. I mean when I see first and second cousins in my Ancestry DNA matches then at that point it's pretty easy to match any unknown DNA sample to their family. You simply don't need DNA from 100% of the public unless it's going to be used for future identification but instant DNA matching is probably decades away and maybe not even possible. It's takes a huge amount of technology and lab work to get DNA code out of a cell.