I reckon there's many many ways to work on the problem - but doing an immediate inventory has limited value - unless you've got a room full of shelves chock-a-block full floor to ceiling as one sees on the TV super couponers.....
for me, a weekly "meal plan" is the basic organizing document. it's just a Word document with two sets of "blocks" - down the left side is the day/meal, in the right block what ingredients I may need to buy.
doesn't take long to do this - it's not really super rigorous. but if you do a roast chicken on Tuesday and figure there will be left overs,,,, Thursday looks like chicken salad / cream chicken over toast / pot pie, etc.
and if I run into something special at the grocery store, the plan changes!
being empty nesters, cooking for two presents a major challenge in 'downsizing' dishes - my idea of a really good meal is: "no leftovers" - fix it, eat it, move on..... there are exceptions - stuffed shells / lausanga gets done in two dishes - one for the freezer. "small cooking" makes the 'plan ahead' thing even more important - I can buy half a head of cabbage, but not half a head of cauliflower.... so I need to have a plan on when we'll be eating up the fresh produce.
I can get pre-prepped veggies in trays - at a significant cost increase. actually I do buy the pre-prepped mixed fruit stuff, time to time - altho it's much more expensive, there's no economy in buying a whole watermelon and throwing half of it in the compost heap.....
obviously one has to keep tabs on perishables, what's in the pantry, etc. but if by 'expiring' you mean a can of soup that's been on the shelf for three years, that's a different problem.
something else you may find useful - I have a list (Word document, easy to add / edit...) of main dishes and side dishes we have prepared and liked. it grows every month - but when you're sitting there pounding your head on the counter wondering "What shall we have . . . " it's often useful to peruse the list - typically results in a "gosh haven't had that in a while."