The only way I can see this working is if GOG uses the "Bandcamp" method. I'm pretty sure most of you reading this knows what Bandcamp is but just in case: Bandcamp sells music, predominantly from indie artists and labels, which you can then download. Like Steam and GOG for games, Bandcamp is geared towards digital consumption.
However, Bandcamp allows artists and labels to sell merchandise along side digital music purchases. This can physical formats like CDs, vinyl and even cassettes. And shirts too.
GOG could encourage developers and publishers to sell physical copies along the digital purchase for slightly higher price than digital alone.
The problem is convincing developers and publishers that it's worth it. In their view, why would spend money printing physical copies for that a platform that went digital two decades ago? Consoles, at least, still have reasons for having an optical drive.
(Fuck you, Sony!)