What should i do to familiarize them with a large cage?

I have a pair of budgies that live in a small cage. I bought them a new, bigger one so they can move around more freely. The female has 3 chicks and 2 eggs. I moved them to the new cage, but they seemed scared, so I quickly brought them back to the old one, fearing they might stop feeding the chicks.

This pair has already produced 7 healthy chicks that grew into healthy budgies. I bought the large cage to discourage them from laying eggs continuously, as the female lays a bunch of eggs about one month after the last egg hatches. It laid three eggs that all hatched, then laid five more, but only four of those hatched. At the moment it laid 5, 3 hatched and still waiting for the other 2.

I want to know what l should do to familiarize them with the big cage.