Is there evidence of gas ever forming a black hole without being a star first? Here's my general understanding of how gas particles form a black hole:
1) Gravity pushes gas particles together.
2) These fast particles create heat (from friction due to them rubbing together?).
3) This heat gives the particles enormous amounts of energy to overcome each others' nuclear forces, creating fusion (a star is created).
4) This fusion counteracts the gravity squeezing the particles inward, creating an equilibrium.
5) Eventually the hydrogen runs out, and fusion stops.
6) Gravity pushes the particles closer and closer, until the collective mass is so dense it forms a black hole.
Question: Has there been evidence of gravity causing gas particles to form a black hole, without becoming a star first? It seems to me that the "star stage" is just an inter-mitten period of sorts, and doesn't aid in helping the particles become a black hole. Of course, maybe it's physically impossible for gas particles to not form a star when getting squeezed to such an extent, but that's what my question is about.
 A: Firstly, we are not going so see this process happening in the present-day universe, because gas clouds with significant metal enrichment cannot collapse directly to black holes. The main reason for this is that gas enriched by metals from previous generations of stars can cool effectively and this leads to fragmentation of a collapsing gas cloud.
The instability that leads to the collapse of a cloud is governed by the Jeans mass, the smallest mass that is likely to collapse, which scales as $T^{3/2}/\rho^{1/2}$, where $T$ is the temperature and $\rho$ the density. If the gas can effectively cool as it collapses, then the temperature remains roughly constant, the Jeans mass falls and the cloud breaks up into smaller cores. These cores usually end up being of stellar size.
The fragmentation ceases because at some point in the collapse, the gas becomes opaque to infrared radiation and the cloud achieves a rough hydrostatic equilibrium. Thermal energy that is lost results in contraction and the centre of the protostar heats up. The problem for black hole formation is that it is not possible for the collapsing cloud to get inside its Schwarzschild radius before it ignites nuclear fusion.
I have done a rough calculation here that shows the interior of the cloud would reach 500 billion K by the time it had collapsed to a Schwarzschild radius, so there is simply no way that this direct collapse can happen. Nuclear fusion would occur and the star would have to go through its life cycle before any collapse can resume.
However, in the early universe, it might be possible for a gas cloud to collapse directly to a massive black hole and this may be why quasars can exist only a few hundred million years after the big bang. 
Primordial gas made of just hydrogen and helium atoms cannot cool very efficiently however, hydrogen molecules can radiate efficiently. The key to direct collapse to a black hole is to prevent the cooling and fragmentation of the gas. This can be achieved if an external source of UV radiation, provided by the first stars, is able to dissociate the the hydrogen molecules. The primordial clouds are then less susceptible to fragmentation because they heat up as they get more dense and the Jeans mass cannot become small. These large clouds are not as dense as a smaller mass cloud as they approach their Schwarzschild radii, so do not become opaque to the radiation they produce and they may be able to collapse directly to large black holes ($10^4$ to $10^5$ solar masses). See this press release for an alternative summary of this idea and links to recent academic papers on the topic (e.g. Agarawal et al. 2015; Regan et al. 2017; Smith, Bromm & Loeb 2017).
In terms of evidence, there is none that is direct. Some would argue that the presence of supermassive black holes only a few hundred million years after the big bang means that these massive "seed" black holes must be created. However, there are other ideas besides direct collapse that could still be possible (e.g. mergers of black holes within clusters) and so the answer to the question in your title must be no at this stage.
A: 
Has there been evidence of gravity causing gas particles to form a black hole, without becoming a star first?

"Chandrasekhar derived a relationship between the star's mass and its radius which sets an upper limit to the mass a white dwarf can have, beyond which it will collapse to a neutron star or, if sufficiently massive, to a black hole. (http://archive.ncsa.illinois.edu/Cyberia/NumRel/BlackHoleFormation.html)"
This is how, traditionally, black holes are conceptualized to form through stellar evolution. I think to form a black hole without first forming a star would require an enormous amount of mass, or a small amount of space. Depending on the specific local conditions, this can happen with 1) supermassive BH formation or 2) in the early universe (these two points are related).


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*At the centers of galaxies exist supermassive BH's. Supermassive BH's are on the order of $10^6$ solar masses. So if we imagine having $10^6$ solar masses sitting in otherwise empty space, I would think that a star would not form since the back-reaction timescale is (likely) to be much less than the nuclear timescale. But this simple thought experiment is not very realistic in terms of physical structure formation. 

*How does structure form in the universe? Two main explanations prevail: monolithic (top-down) and hierarchical (bottom-up).
(http://iopscience.iop.org/article/10.1086/305523/fulltext/) 


Monolithic was the original explanation, but nowadays hierarchical formation is more favorable (monolithic is not yet completely ruled out). 
(https://ned.ipac.caltech.edu/level5/Sept05/Gawiser/Gawiser1.html)
"The original model of galaxy formation was Monolithic Collapse (Eggen et al. 1962), where gravitational collapse of a cloud of primordial gas very early in the lifetime of the Universe formed all parts of each galaxy at the same time. Modern evidence rules out this model on two fronts; the widely varying ages of different components of the Galaxy provide a counter-example, and the LambdaCDM cosmology predicts "bottom-up" i.e. hierarchical rather than "top-down" structure formation."
For hierarchical formation:
(http://burro.cwru.edu/Academics/Astr222/Cosmo/Structure/hierarchical.html)
(https://starchild.gsfc.nasa.gov/docs/StarChild/questions/question55.html)
