Humans can tolerate a maximum pressure of 100atm, but it becomes uncomfortable above 30 atms. Deep divers usually wear protective equipment like goggles among other things and our eyes seem to be more fragile than the rest of our body.
So, without using goggles how deep can a human open their eyes under water before suffering from an injury?
The injury, I believe, would be the eye getting crushed by external pressure.
Crushing damage from pressure occurs due to pressure differences. Imagine you have a rigid container. If you have equal gas pressure inside and outside, the pressure acts on just the walls and the container will survive unless the pressure is high enough to heat/melt the walls to failure. However, if you have high pressure outside and low pressure inside, you can expect the vessel to at some point violently collapse due to the pressure difference.
When diving with a mask, it's important to equalize the pressure inside and outside the mask. E.g. from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4943308/
Diving can affect the IOP [intraocular pressure] in a number of ways; firstly from the change in the internal mask air pressure at different underwater depths, secondly from the inhaling or exhaling from the nose, and thirdly through the diving mask itself. The first and second factors can be controlled by the diver by exhaling from the nose during descent, also known as equalizing the mask pressure. Senn et al. [5] found that diving mask pressure spikes were less common in experienced divers compared to beginners. Failing to equalize the diving mask pressure can lead to ocular barotrauma, which ranges from lid edema, ecchymosis and subconjunctival hemorrhage to more serious injuries such as hyphema and subperiosteal orbital hemorrhage [6, 7]. The diving mask itself may also affect the IOP. Swimming goggles are known to increase the IOP, with larger-frame goggles having less effect than smaller-frame ones [8,9,10].
Or from https://www.ncbi.nlm.nih.gov/books/NBK545224/
Mask squeeze is a type of facial barotrauma injury that occurs most commonly while self-contained underwater breathing apparatus (SCUBA) diving or freediving. This condition occurs when divers fail to equalize pressure in the face mask to the surrounding water pressure as they descend. The result is a negative pressure (relative to the surrounding water pressure). The difference in pressure inside and outside the mask can lead to injury of blood vessels and tissue of the eyes and tissue covered by the mask, including forehead, nasal areas, and periorbital regions. The main risk factor for a mask squeeze is the inexperience of the diver. Masks with high internal volume or the use of snorkeling masks or swim masks that do not cover the nose can also increase the risk of this type of injury.
Or, in simpler phrasing, if you have low pressure inside a mask and high pressure inside the rest of the body, the pressure difference is going to push/suck the eyes outward and crush the blood vessels or damage the eye itself. You want to have the same pressure pushing on the eyes from the outside and inside. It's really no different if you 1) have high pressure outside the mask and 'normal' pressure inside the mask, or 2) have low pressure (vacuum) inside the mask and 'normal' pressure outside: both situations have a pressure difference, and it's the difference that does the damage.
So, to answer your title question, a mask is more likely to increase pressure risks to the eyes rather than to decrease it.
Goggles do not, cannot, protect eyes from pressure. The pressure on both sides of goggles should be nominally the same. In fact, divers tend to use a mask, which communicates with the nose, to be able to equalise the internal pressure with ambient easily, rather than goggles which can damage the eyes if a descent is made without awkardly adding air by exhaling bubbles while lifting the lower edge of the goggles. The only thing that can isolate you from pressure at depth is a rigid suit, or a diving bell.
So why do people wear goggles/mask underwater?
The main reason professionals wear them is to keep a layer of air in front of the eyes, so that the eye lens is working between the correct refractive indexes and giving you normal vision. Replace that air with water and everything becomes very blurred. Basically the front face of the eye lens stops bending light, so you become extremely long-sighted.
The main reason amateurs wear them is to avoid the yuk factor of opening eyes under water, or irritation from biocides in the swimming pool.
There are multiple things that limit the depths divers can reach, but none involve the eyes.
Oxygen toxicity and nitrogen narcosis limit compressed air or nitrox sport dives to a few 10s of metres. To go deeper one needs extensive decompression time and/or expensive helium, and deeper still an addition of hydrogen. Regular commercial dives rarely exceed 300 m, with only the military accessing anything approaching 500 m. Studies (usually in pressure chambers on land) have pushed lower, but seem to run out of human tolerance for the effect of high pressure gases on the central nervous system in the 650 to 700 m range.
I did a short diving course, and the exam started with them throwing all the gear into the pool, mask included. The idea is that you need to be able to recover from an accident where everything is knocked off your face, and then some. So, open your eyes, swim to the bottom, locate blurry tank and take a breath, grab your blurry weight belt, locate blurry mask and put it on, breathe air into mask so now you can see properly, and it gets easier from there.
Currently the record for the deepest dive wearing scuba equipment is 332.35m. The descent took only 15 minutes while the ascent lasted 13 hours 35 minutes.
Liquids do not compress, so the sinuses, inner ear, lungs and circulation are in far more danger from pressure than the eyeballs.
The main danger is not the pressure at depth, it is the readjustment to the expanding gases as the diver rises, decompression sickness, which rarely affects the eyes.
