Here are two plots from a 2010 paper "Long-Periodical Variations of Earth Rotation, Determined from Reconstructed Millennial-Scale Glacial Sea Level" by Chapanov & Gambis. They start with published sea level data for the past 380 thousand years and then translate mean sea level to excess LOD (Length Of Day) based on a model of earth rotation.
You can see that sea level varies periodically by up to 100 meters. And according to their model the rotation of the earth varies by up to about 200 ms per day. If UTC existed back then as much as one leap second per week would be required.