Let's remember that ca. 6000 years ago (4000 BC) those people were few in numbers. Rb-M269 and R1a-M198 formed respectively ca. 13600 and 14300 years ago, but for more than half of their history they remained very few in numbers, most likely undergoing many demographic bottlenecks during that time. Only later, in period ca. 6000 - 4000 years ago (4000-2000 BC), they - apparently together (at least at the beginning) - underwent a huge a demographic expansion, greatly propagating both in numbers (begetting dozens of new very successful lineages) and in geographic extent (spreading over most of Eurasia, as we know from aDNA and modern distribution).
Probable TMRCA shows when a given male lineage started to expand in numbers after the last severe bottleneck:
http://www.yfull.com/tree/R1b/
R-M269 formed 13600 ybp, TMRCA 7000 ybp
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R-L23 formed 7000 ybp, TMRCA 6300 ybp
R-Z2103 formed 6300 ybp, TMRCA 6100 ybp
R-L51 formed 6300 ybp, TMRCA 5700 ybp
R-L151 formed 5700 ybp, TMRCA 5100 ybp
R-U106 formed 5100 ybp, TMRCA 5100 ybp
R-P312 formed 5100 ybp, TMRCA 4900 ybp
R-DF27 formed 4900 ybp, TMRCA 4900 ybp
R-L21 formed 4900 ybp, TMRCA 4700 ybp
R-U152 formed 4900 ybp, TMRCA 4600 ybp
http://www.yfull.com/tree/R1a/
M-198 formed 14300 ybp, TMRCA 8400 ybp
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R-M417 formed 8400 ybp, TMRCA 5400 ybp
R-Z645 formed 5400 ybp, TMRCA 5000 ybp
R-Z282 formed 5000 ybp, TMRCA 5000 ybp
R-Z280 formed 5000 ybp, TMRCA 4800 ybp
R-Z93 formed 5000 ybp, TMRCA 4600 ybp
R-Z94 formed 4600 ybp, TMRCA 4600 ybp
R-Z2124 formed 4600 ybp, TMRCA 4600 ybp
R-M458 formed 4600 ybp, TMRCA 4500 ybp
R-Z284 formed 4600 ybp, TMRCA 4300 ybp
Between ca. 6000-5500 ybp (4000-3500 BC) and ca. 4500-4000 ybp (2500-2000 BC) things get rapid.
In that period a lot of new successful descendant lineages "pop up" in a short timespan.
But expansions of those male lineages were not necessarily massive migrations of numerically large populations. Those could be patriarchal clans ruled by powerful chieftains, migratng and propagating their offspring after having settled/conquered.