On a web browser it is indeed more straightforward, you have to specifically select the boarding pass option there. On the App a pop up comes up after check-in confirmation (do not select the one-screen option if presented, select the Change Seats option further down). The problem with the pop up is that there is a pregnant delay before it comes up, and if you pressed the screen to move information (etc) then you risk fat finger syndrome. But go carefully and slowly on the App and that will be fine too.

I would check in without looking at seats to begin with, then start from the beginning again where you should be given a Change Seat dropdown. That dropdown does not present it self immediately, you have to go back into MMB. Theoretical Seating generally gives you the best option anyway, given your status (or lack thereof!). But yes, just check-in at the first moment, then keep monitoring the seats. A big percentage of seats change in the first few hours, so other options may come up for you. Don't avoid OLCI however, unless it won't let you do it anyway, which is sometimes a sign of an upgrade coming your way.