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When and where did matter in liquid state first appear in our universe? Liquid has never been a global state of the universe, but it certainly appears nowadays locally in some places. As far as I know, liquid currently only exists on planets, but I can well be mistaken. I can imagine a couple of different possibilities for first appearance:

  1. After the first generation of supernovae there were heavier elements outside stars and they could form planets with suitable composition to have liquids.

  2. Perhaps there were early gas planets of suitable size around the time that stars started forming that produced suitable conditions for liquid hydrogen inside. The outer layers would be gaseous, but perhaps pressure could produce liquid inside.

  3. If the previous scenario is impossible without an external source of heat, maybe during the first generation of stars it would have been easier.

Or perhaps it was something else. I am not looking for a transient situation which could be vaguely be described as a liquid for a fraction of a second. Instead, I am looking for something in or close enough to equilibrium so that the liquid stays around for at least a minute and there is at least a liter of it. Feel free to adjust the parameters, but I hope my intention is clear enough.

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Have a look at a paper 1312.0613 by A. Loeb. He considers possible existence of rocky planets with liquid water as early as $100<(1+z)<137$ (about 10-17 million years since Big Bang).

From the footnote 2:

After the first stars formed, the subsequent delay in producing heavy elements from the first supernovae could have been as short as a few Myr. The supernova ejecta could have produced high-metallicity islands that were not fully mixed with the surrounding primordial gas, leading to efficient formation of rocky planets within them.

So the mechanism for liquid formation would be OP's item 1.

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