Primates generally and monkeys in particular are social animals, traveling in troops, sharing resources.
Thus it is likely that if ONE primate S.American monkey ancestor reached the "new" world, then it is likely that several did.
There has not been one piece of evidence that shows that such an event was impossible.
The presence of New World monkeys shows that some form of communication occurred between the Old and New worlds. The exact method is not even that important (except as the topic of this thread, of course).
To repeat: The presence of New World monkeys shows that some form of communication occurred between the Old and New worlds.
If creationists want to overturn this fact (as fact it is) they will have to overturn a lot of other scientific facts as well, starting with the documented common ancestor between Old and New world monkeys.
But all we see are claims, without supporting evidence. That's not going to overturn any observed facts. All the "what ifs" they can come up with are not worth a single verifiable observation--and science is based on verifiable observations. Making such observations, and then explaining them, is what science does!
But creation "science" is designed to cast doubt on scientific findings, by any means necessary, when those findings contradict, or fail to support, religious beliefs.
We often see creationists changing the meaning of terms or complaining about the scientific method--all in an effort to include scripture or "divine" revelation as scientific evidence so that their particular beliefs are supported by "science," when now they are not.
Summary: The exact method by which New World monkeys got to the New World is not critical to science. Without supporting evidence, the "what ifs" of creationists are not even of much interest to science.
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.