Do you need to break in climbing shoes?
You do not normally need to force the break in period of climbing shoes, this will happen naturally by wearing the shoes and climbing in them.
There are of course different methods for breaking in climbing shoes faster, but, they are optional and not required. Some methods could even be harmful for your shoes.
Whether your shoes need to break in or not depends on the type of shoes you bought and the size. If you bought shoes that are synthetic, don't expect any noticeable change even after 6 months of climbing in them, since synthetic shoes don't really have much of a break in period, and if they do, it's very minimal. This should also be a determining factor when buying climbing shoes, since you probably won't want to size down synthetic climbing shoes, expecting them to stretch.
Leather shoes, on the other hand, do stretch quite a bit, so if you bought leather shoes, and you sized down, then you should expect a break in period.