The last ice age peaked at 20,000 years ago. The people who survived in pockets of survivable territory started to repopulate Europe in the period from 14,000 to 7,000 years ago, called the Mesolithic era. Several ancient genomes are now available from that era. They suggest that the effective male population size prior to the repopulation of Europe was just 30 men.
Thus, modern humans only barely hung on through the Ice Age in Europe, and ultimately, their ancestry makes up a fairly modest share of modern European ancestry.