jacksepticeye
Member
Comstock may not have had a child already, but he - or the Luteces - probably figured that there exists a universe where
A) Booker has a child
B) He lives in a place that Comstock-Booker knows where to find him (his detective office).
And thus the Luteces, with their awesome knowledge of how tears work, helped open a tear to such a universe.
As for why they didn't just take any random child, I believe it's mentioned that for some sciencey reason or another, Comstock needed a biological child of his.
Seems like a bit of a plot hole TBH. Maybe the Luteces already found comstock in the past/alternate time and kept an eye on him.