An "uncontested" divorce can be handled in a couple different ways:
1) By default: One party (the Petitioner) files and serves the other party (the Respondent). The Respondent does not file any kind of response, and the Petitioner files to have the court proceed by default and finalize the divorce based on the terms in the Petition. Generally, default requires a brief hearing to make the case final; or
2) By consent: The Petitioner files and serves the Respondent. Both parties sign a Consent Decree at the end of the case and submit it to the judge (no hearing) and the judge signs it to make it final.
Either way, the soonest a default hearing can be held (or the soonest a Consent Decree can be submitted to the judge) is 60 days after the Respondent was served with the documents (this is the "cooling off" period).