A reader in the comments reminds me there has been a preprint which is relevant to the population structure of Baltic Europe which came out a few months ago, Extensive farming in Estonia started through a sex-biased migration from the Steppe:
…Here we present the analyses of low coverage whole genome sequence data from five hunter-gatherers and five farmers of Estonia dated to 4,500 to 6,300 years before present. We find evidence of significant differences between the two groups in the composition of autosomal as well as mtDNA, X and Y chromosome ancestries. We find that Estonian hunter-gatherers of Comb Ceramic Culture are closest to Eastern hunter-gatherers. The Estonian first farmers of Corded Ware Culture show high similarity in their autosomes with Steppe Belt Late Neolithic/Bronze Age individuals, Caucasus hunter-gatherers and Iranian farmers while their X chromosomes are most closely related with the European Early Farmers of Anatolian descent…
As you can see in the PCA plot above the Comb Ceramic Culture and the Corded Ware culture in Estonia are modeled well by the three ancestral populations hypothesis for Europe. The problem with this is that Finns and Russians with Finnic background do not fit with this model. There has been clear later gene flow.
From the text:
Interestingly, modern Estonians showed a bigger proportion of the blue component [associated with European hunter-gatherers] than CWC individuals. Comparing to CCC individuals, modern Estonians lack the red component [Eastern Siberian]. This, together with the absence of Y chromosome hg N in CCC and CWC, points to further influx and change of genetic material after the arrival of CWC.
The sample sizes are small. Additionally these are from Estonia, not Finland. But the Comb Ceramic Culture was widespread throughout the region.
Also, from a 2015 paper (supplements):
Among the northern Europeans, the Finnish (finni3) show evidence of an admixture event involving a minority source most similar to contemporary North Siberians (469CE (213BCE-1011CE)). Finns are thought to have originated from the northward migration, and subsequent contact, between Central Europeans and indigenous Scandinavian hunter-gatherers closely related to the Saami [S33]. The Saami are closely related to the individuals that make up the North Siberian world region, and whilst our confidence in this admixture date is low because of the small size of the cluster, the event we see is likely to represent this key period in Finnish history.
The “North Siberia” cluster are: Selkup, Chukchi, Dolgan, Ket, Koryak, Nganassan, Yakut and Yukagir. The admixture is very recent. I suspect too recent. But it gets us to the qualitative point that the Siberian admixture into Finns is probably not that old.
Related: The Origin of the Finnic Peoples.