Adding to my own post: There are a ton of reasons to do this in two sections. Practically, if you start hitting places piecemeal you will miss some. Since they are illegal they have much easier times of going underground or just moving, You will have a lot more people able to avoid sweeps if you are doing it like Trump did on his first term. This was a weakness laid bare during said term and Trump's people have had 4 years of being able to plan how to do it better.
Optically, it also works better doing it this way. The first ones taken are the scum of the scum, that Haitian illegal who got taken is now plastered all over Facebook and Twitter. -That- is now the face of the people being deported. The left tried to get ahead of this by showing the obviously staged Illegal mothers weeping but it gained no traction. And since ICE is consciously going around the large communities and just mapping them out... by the time they finally get to the big sweeps it will be thoroughly ingrained in people's minds that the current crop are like that crop. It narratively completely undermines the media attempt to spin it and make hay, especially if when they do the big sweeps they can avoid leaving any stragglers to interview about how "My mother and father just wanted a better life!"