As at the end of the last Iceage the ice receded and water level lowered in the Baltic sea basin area, the Baltic sea area was inhabited from the South-South-West by Western hunter gatherers, and from the East-South-East by Eastern hunter-gatherers.
The most common paternal Y-DNA haplogroup of modern Estonian men is
N (Eastern Hunter-gatherers), among 34% of tested,
I (Western Hunter-gatherers) among 15% of tested,
R1a (associated with Yamna culture, found most in so-called Slavic nations) among 30% of tested.
The oldest attested evidence of post glacial settlement of Scandinavia dates from 11,000 BC, of Estland dates from 9800 BC.
Archeological evidence shows that the Western hunter-gatherers from ice-age refurgia around the Mediterranean sea and Iberia, that was the area of Europe least effected by Ice age, started expansion to the North along the Western coast of Europe (34000 ybp – Paglicci Apulia, Italy; Y-DNA: I; mtDNA: H). 
The Eastern hunter-gatherers arrived from East-South-East (45000 ybp – Ust Ishim, Russia: Y-DNA: K2a / NO; mtDNA: R) over Ural mountain foothills over icelakes and rivers, over the modern East-European plane West-South-West. 
They stayed over the iceage in the Black sea refugia, with propably seasonal raindeer and seal hunting on the banks of the ice sheet and along the icelakes and rivers, until the climate warmed enabling to inhabit the lands to the North (37000 ybp – Pestera cu Oase, Romania: Y-DNA: K2a / NO; mtDNA: N). 
The most common mtDNA (maternal) line among Estonians is -:
U (associated with Eastern hunter-gatherers), found among 24.5%,
V (associated with Eastern hunter gatherers), found among 8%,
W (associated with Eastern hunter gatherers), found among 3%,
H (associated with Western hunter gatherers), found among 43.5%,
J (associated with spread of agriculture from Balcans and Near-East) found among 10% of tested
Eastern hunter gatherers and Western hunter-gatherers met in the Middle of Europe during the iceage (31000-34000 ybp – Krems, Austria: mtDNA: H and U). Inhabiting gradually to the North. Sadly due to cremation burial customs of the both pagan religions not many archeological material with preserved DNA has not been found to determine the borders of the nations more exactly.
So – it can be concluded that the modern day Estland people (>80%) have cultivated their land and developed their culture on the shores of the Baltic sea for over five thousand years, are indigenous Central and North-European people with ancestors inhabiting Europe already 34000-37000 ybp.
* “ybp” – “years before present” – aastaid enne praegust
 – Callaway, Ewen & Nature magazine (23 October 2014). “45,000-Year-Old Man’s Genome Sequenced”. Scientific American. Retrieved 24 October 2014.
 – Fu, Qiaomei; Posth, Cosimo; Hajdinjak, Mateja; Petr, Martin; Mallick, Swapan; Fernandes, Daniel; Furtwängler, Anja; Haak, Wolfgang; Meyer, Matthias (2016). “The genetic history of Ice Age Europe”. Nature. 534 (7606): 200–205.