Can you show us a photo of your tank? Often fish hide because they don't feel safe, so you could modify the scape in this tank to help them feel safer.
I don't recommend getting a bigger tank and scaping it with no hiding places, it would be better to get a bigger tank and scape it with lots of hiding places and research what the corydoras would feel most comfortable living in and making it with all those features - generally the more hiding places a fish has, the more comfortable they feel add they know they can easily hide if needed. When you create a naturalistic tank, you get more natural and interesting behaviour.
Another option might be to get a group of small schooling fish, I have kuhli loaches which were very very shy and never came out, then I added some cardinal tetras and suddenly I see the kuhlis all the time - they use the tetras as a sign that everything's safe weekend the tetras are out.
I think the best option would be to get the bigger tank, scape it according to their needs (with hiding places), buy a few more (they are always happier with a bigger group), and buy some dither schooling fish to make your tank corydoras heaven!