While I agree with that it's hard to make definitive statements about language relationships past 10K years, it's pretty well accepted that Proto Indo European existed around 7K years ago.
By 5K years ago, it's primary subgroups, i.e Hellenic, Slavic, Germanic, Italic, and Indo-Iranian were already forming.
Didn't this process last a very long time though? IIRC the current consensus seems to be that Anatolian split off very early but Baltic/German/Slavic staid on the same branch until quite late (maybe even as late as 1000 BC) with other groups somewhere in between.
Na-Dene and Yeniseian languages are theorized to be part of a common family and the evidence is pretty good; they come respectively from America and Siberia. See https://www.science.org/content/article/land-bridge-connects... for some more information.
Unless those populations only started using language once they had set foot in North America, which would be an even greater thing to push.
Edit: wiki link https://en.wikipedia.org/wiki/Den%C3%A9%E2%80%93Yeniseian_la...
First link was proposed by Merrit Ruhlen in 98. People have opinions about him but he and his mentor Greenberg did very well received work on African comparative ling
Ed Vajda brought rigor to the hypothesis in series of publications which established Dene-Yenesian through the comparative method starting in 2008 and continuing to the present. Nichols briefly and favorably reviews this bibliography in her paper. As a senior researcher in the field, she was one of Vajda's original advocates when his proposal made its splashy debut.