I know of people who have taken the children immediately, and then had the approval later from SS. It depends really on the circumstances.
Does your cousin currently have 'rights' over this baby, or has the baby been 'removed' to the care of SS?
The time delay is because anything that needs approving needs approving through a panel, and I think it's a two-stage process, and the panel doesn't sit very often.
Generally it is 'bad' for children to be moved around, or to be in placements that don't work out; hence the caution. Research shows that young babies who are in temporary care (below age of 1 year I believe) go on to suffer no ill effects when they are transferred to permanent care, as long as they were in a stable, warm, loving environment.
This is why SS would rather have the baby somewhere settled with a possible delay of 4 months before going somewhere permanent, rather than risking a placement breakdown.
Does that help?
Having said all that, generally with SS nothing will happen very fast unless you keep pushing.