Could we parallax measure stars just based on the Earth's size? Imagine two major surface observatories, perhaps the "northermost" and "southernmost" such (ideally on a similar longitude).

For nearby stars, could they each take a photo at the same time, and achieve a distance measurement to that star, based on about the size of the Earth as the baseline?

(I appreciate that either of the scopes need only wait a few days, for their viewpoint to have moved a much longer baseline distance!)

Or is that distance far too short?

What then is about the minimum baseline we could parallax-measure the nearest stars, with our currently best telescopes?  100,000km, a million? Far more?
In principle, it's not impossible.

The Gaia spacecraft, designed primarily for measuring stellar positions, is able to measure parallaxes up to 10 kpc away with 20% uncertainty. Its baseline is 2 AU; $2.3\times10^{4}$ times larger than the diameter of Earth. Thus, placing two Gaias on each side of Earth would be able to measure parallaxes of stars up to a distance of $10\,\mathrm{kpc} \,/\, 2.3\times10^{4} \simeq 0.4\,\mathrm{pc}$, meaning that you would almost be able to measure the distance of our nearest neighboring star, $\alpha$ Centauri, which lies at 1.3 pc. So you would just need improve your Gaias a little bit.

This ignores small complications such as the atmosphere, but if you're willing to put them outside the atmosphere, you could do it. Of course, it would sort of be a waste of time, since we already know the distances to the nearest stars, but hey, go ahead.