And then I also read the book Deep Ancestry by an expert in the field Spencer Wells. According to him G2a entered Europe around 15.000-10.000 BC and when the last Ice Age came the R1b and G2a people moved south and after the ice melted repopulated Europe. So according to him the G2a western Europeans are descendants in the male line from Paleolithic Europeans. So way before the Neolithic.
Since Spencer Wells studied this and is a doctor in this field, shouldn't we believe him? But his theory is not mentioned often. See page 210/1 of his book.