There has not been a complete 6,000 years since the beginning of creation. In the millennial week of this present creation, we are in the 6th millennial day. Sabbath Millennial Day is next.
The ice in Anartica and Greenland did not take such time as you think, to form, and just over 4,500 years ago, the entire globe was covered with the waters of the flood of Noah to 15 els above the highest mountain on earth -even those in the polar regions.
Also, there are ancient maps of the entire globe that were done by satellite, and you can find the reproductions of them in the Book "Maps of the Ancient Sea Kings", in which Antarctica is depicted ice free, and divided by water into two land masses.
That map was made post flood, so the ice was not formed there, yet...
FYI: God began the process of dividing the one land mass of creation into several, separated by the waters, after the fall of the tower of Bab-el and the dividing of the one mother tongue. At that time, God cut off/shortened the long days of Adam persons and divided the land mass into the several there are now.
That was depicted by Eber in his naming two sons "Cut off and Divided" Yoktan and Peleg.
Jasher Chapter 7 - The Book of Jasher Published by J.H. Parry & Company 1887
Book of Jasher chapter 7: 19, These are the generations of Shem; Shem begat Arpachshad and Arpachshad begat Shelach, and Shelach begat Eber and to Eber were born two children, the name of one was Peleg, for in his days the sons of men were divided, and in the latter days, the earth was divided.
20 And the name of the second was Yoktan, meaning that in his day the lives of the sons of men were diminished and lessened.
A WW 2 crashed plane was discovered some decades back, under about 200' of ice. I may remember details a bit wrong, but it defied the so called "experts" of how long it takes ice to form in the polar regions. I read it in an Answers in Genesis paper.
Maps of the Ancient Sea Kings