How are you printing? Most of us don't use cardboard - we print on a platen attached to a press and partialy dry using a flash cure before curring fully.
I am assuming you are using air dry inks, printing on a table? Flat drying is best if the ink is still very wet, but you might want to replace the cardboard with some other form of board that wont go soggy.
You would be best to find some way to remove some of the moisture to get past the 'wet' stage. A hair dryer is better than nothing, a heat gun better but be careful not to start a fire. Some hobby inks will allow you to use an iron to cure the print. Just cover it with a piece of baking paper.
I am using water based fabric ink. It says to dry between colours. I am not a professional yet. Starting out with basic equipment I have 32 t-shirts to do. I am putting a design on then writing on top. Can I put the writing on without drying the design first? I can iron to set the final print.
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