The phrase "already moist" is correct and usable in written English.
It can be used to describe something that is wet or damp at a particular moment, often implying that it was moist before a certain action or event took place.
Example: "The cake was already moist before I added the frosting, making it even more delicious."
Alternatives: "previously damp" or "initially wet".
Since the region had received substantial rain in November and December, the ground was already moist, limiting its ability to absorb water.
Taking a warm shower or bath can help a runny nose because air you're taking in is already moist and warm, so the membranes can relax and stop secreting water and mucus.
We flap at them with gloved hands, but, already moist from the rain, everything now turns muddy.
The increase of LWP based on absolute change of MAP became flatter along the humidity gradient (Fig. 2B) because additional rain was less important for maintaining the soil moisture of an already moist soil in the more humid regions.
There is no need to water after rainfall or when the soil is already moist.
Too much love can kill your plants, so stick your finger in the dirt before you water to see if it's already moist.
The crumb is far from "crisp", as the packaging claims, but it does provide further savoury depth to what is already a moist egg of well-seasoned complexity.
You should be able to refrain from blinking for a few seconds, because the eye is already very moist from the tears.
Tony Morante paced near Gate 4 at Yankee Stadium early Friday afternoon, his eyes already red and moist.
Peggy Nabbefeldt, the marketing director for Cottonelle, said that one out of four Americans already used a moist tissue after they use the toilet.
Given that Portas said she had already found "a moist rubber gimp outfit in a Tesco bag" in one of the rooms and been asked if she could provide "company" for another guest, Woodburn's unshockability might be tested a little.
