First, welcome to the Forum. It is always great to have new members on here, and, because my favourite frogs are African Giants, I am always excited to hear of more members owning them.
Depending on the size of the frog, 10 gallons is more than adequate. These frogs are not hugely active and only need enough room to not feel squished and to house an appropriate sized water dish. My female and one of my males are in a 10 gallon; my other male is in a 15 gallon and they all have room to spare. Depth of soil is hugely important to them, as they love to dig.
Having his eyes closed does not mean that he is in aestivation. It could be a sign that conditions are drier than he likes, but frogs also sleep and have a protective membrane that covers their eyes in the process. As Kevin says, unless he is buried deep and has a paper-like membrane around him, he is not in hibernation. That is usually only brought on by dry conditions or in extreme temperature variations or both. Give him a good misting and his eyes will open.
A picture would be great, and if you could get an SVL measurement, we could recommend an appropriate size enclosure for him.





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