I write with no particular authority, but I do not polish my shoes immediately. As discussed in several threads, well-tanned leather is potentially a maintenance-free product.
I wear them for a few days around the house to start the break-in process, then progress to longer wearings outside of the house. My motivation is to allow time for any defects to reveal themselves that might necessitate a return that could be compromised by any alteration of the shoes (e.g., conditioning and polishing) on my part. At the first excuse, which is usually some exposure to rain, I give the shoes a thorough going over with AE conditioner (almost all of my shoes have been replaced this year with AE) with an especially liberal application to the nascent creases. This essentially strips off the factory finish (based on the appearance of the shoe and the rag afterwards), which is then replaced with color-matched cream. If experience has thus far suggested a problem with water spotting, as it did with my black AE Harrisons, I apply a coat of neutral wax.