The default case for a U.S. patent application is to be published 18 months from the earliest claimed priority date. That might be 18 months from filing. In the case the priority document was a provisional application and a non-provisonal application is filed just before the 12 month point, the publication will be 18 months from the provisional filing or 6 months after the non-provisonal filing.
In the U.S. there isn't really a third party per-allowance challenge the way there is in many other countries. With the AIA we now have a way to submit a certain class of prior art during a particular time window via a process that obliges the examiner to look at the submitted material. Their is not an ability to present arguments but there is a limited facility to express why and what about the references are relevant.
There is also an older, little used mechanism called a protest that can only be filed in a different time wind. It can only be filed pre-publication. It needs to identify the application. In most cases per-publication no one even knows the application is filed. You can learn more about it here.