Just to get it out of the way at the outset, buying another piece of ply is certainly the most direct solution and possibly even the fastest.
Most of use will at least want to try to salvage the piece so here are some suggestions. These may or may not work well enough for use in the original project1.
With a spill like this there are two issues to face: the dark stain from the coffee and the fat contamination from the cream. Both are tackled to some extent by an obvious first step and that's to simply wash down the surface2, the same way you'd wash down any surface that you'd spilled creamy coffee on.
The coffee component will have stained the veneer and it's possible (probable in fact) that the staining will go deep enough that it can't be removed entirely by washing. On solid wood you could plane, scrape or sand until you're below the affected wood but this isn't possible on veneer.
Bleaching e.g. with common household bleach may reduce or remove the rest of the coffee stain, but ideally I'd save this step until after degreasing, to give the bleach the most uniform access to the wood. Remember the water content of any bleach tried.
Now to the fat, degrease with acetone if you have it. If not use grain alcohol, denatured alcohol (UK: methylated spirits) or mineral spirits (UK: white spirit) in roughly order of preference. Do this ASAP3.
Once you have a surface that water doesn't bead on you've done enough and you can assess how you did on removing the visible staining.
If after cleaning, degreasing, any bleaching and light sanding or scraping the stain is still very evident here are some options:
- If possible, flip the plywood over and use the other side as the show side.
- Use more coffee (black!) to stain the rest of the face similarly. In some scenarios it will be impossible to remove the dark ring from the edges of the initial spill.
- Use actual wood stain, dye or "gel stain" to colour the wood dark enough that the coffee stain becomes unnoticeable. Anything as dark or darker than e.g. Jacobean Oak or Dark Walnut stands a chance of obscuring the remaining staining.
1 The stained plywood isn't a write-off. It can be saved for something utilitarian like workshop cabinets or cut down for jigs etc.
2 Care must be exercised here as some plywoods can tolerate lots of water while others cannot (note, sometimes even if classed as waterproof or water-resistant). So it's highly recommended to test on some offcuts, scrap or non-show surfaces how tolerant your ply is prior to using much of any watery liquid — this includes household bleach and peroxide.
3 With milk and some other dairy whiteners you need to do this before the caseins begin to set, after which you're never getting the stain out :-) With heavy cream the casein content is extremely low apparently (possibly zero) so this is less of a concern than otherwise.