I don't believe that to be true. Under either approach there...

I don't believe that to be true. Under either approach there would be no objective evidence immediately to move the value away from initial value. Remember under both initial recognition would have to be FV with the presumption that purchase price is that (should be no day 1 gain if that assumption holds true). If by the next reporting date the estimate of cash flows changed measurement would change under both approaches. Changes in characteristics of the debt between the two dates could lead to a change in expected cash flows even if no cash yet received - I.e. if that characteristic has a clear linkage to an improvement or decline in expected cash receipts - actuarial modelling would likely be employed in determining those cash flows under either approach. The shorter the timeframe between purchase and balance date the less time to evidence changes that would lead to an altered state of cash flows.

It's worth highlighting that amortised cost requires an initial estimate of cash flows. Given they are acquired at deep discount those cash flows are expected to be significantly less than par. The discount rate that exactly discounts those estimates to purchase price is the effective interest rate. A month later new information will be later that provides a better/new estimate of those cash flows. They are discounted at that original EIR, the difference is a gain or loss to the p&l.....