This ice core data from Greenland shows the climate fluctuations, and also shows how sea level has actually changed . The peaks are when it was warm, the lows when it was cold. Sea level mostly followed this pattern.
We know this due to many sources of evidence, with tide history data showing it with out any doubt..
You can see the peak around 7000 years ago, (Holocene Climatic Optimum) and why sea levels dropped after that, with several more periods where it rose, but then continued to drop. This maximum sea level period is called the Holocene Transgression.