Depends on the timing of hiring and the school, but its not at all uncommon for them to take someone in the first year or two. Of course, some schools only allow professors to take a student every x number of years, so there is some variability.
In fact, many assistant profs seem anxious to get as many grad students as they can reasonably sustain. They're vying for tenure, and 1) Generally need lots of help getting a new lab off the ground and 2) Reasonably expect to be co-author on an additional 1-2 publications for each student they accept since they'll be running master's and dissertation studies.
I'm doubtful any prof gets tenure solely on the basis of the work their students do if they aren't doing good work themselves, but I can't imagine another publication or two and evidence that you're helping your grad students succeed could be viewed as anything but a positive.