DESeq2 (as pointed out in the manual) assumes raw counts. If you only have these normalized counts you might transform them to log2 scale and use the limma-trend pipeline (see limma manual and countless posts on "starting from normalized counts"), to get DEGs with statistical support. Still, for reproducibility you need access to the raw data I think, keep that in mind.
I can't vouch for how good an idea this is, but you can supply custom normalization values instead of letting DESeq normalize. If you supply all 1's for the normalization values, that might get DESeq to understand that it is now looking at normalized data, and it shouldn't change the values at all.