An interesting case is that of Guangfa Wang. He visited a fever clinic, wearing an N95 face mask. However, he did not have eyewear. A few days later, he was diagnosed with COVID-19.
With this in mind, it is possible that one can contract the infection through eyes if the eye membranes come in contact with contaminated fluids or cough droplets.
The downside of this hypothesis is that there is little evidence supporting sole viral transmission through eyes. It is not possible to control for that experiment, given that there is no way to prove the pathway of the virus into the body - either via eyes, mouth or nose.