It's difficult because of the presence of substances that interfere with protein assays (detergent, reducing agent, dye). The approach I would take would be to run the samples on SDS-PAGE, transfer the gel to the Western membrane, stain it temporarily with Ponceau S, and photograph the stain in white light with a gel documentation instrument. Then you can integrate the density of all the bands in each lane as if they were a single band. Then you can destain the membrane and use it for immunoblotting.

It is generally very difficult to determine the concentration of samples in SDS-PAGE loading buffer because the SDS content, reducing agents and (especially) the bromophenol blue dye interfere with most assay to varying degrees. The only assay type that I am aware of which allows quantification of protein concentration in SDS-PAGE loading buffer is the Pierce 660 nm assay sold by Thermo. https://www.thermofisher.com/order/catalog/product/22662

Thank you Adam B Shapiro and Samuel Davis for your suggestions.

You can also using something like this to determine the load after running SDS-Page/transfer to blot:

https://www.licor.com/bio/reagents/revert-520-total-protein-stain