You could ship better crypto (and updated CAs) with your app for Android -- then you could get support for whatever you like on all versions. But it might not use hardware acceleration if available, and hardware running Gingerbread needs crypto acceleration if available. TLS 1.3 isn't all that much code if you can use the system x.509 and system ciphers, or maybe pick one or two ciphers to ship if they're not there; I'd guess TLS 1.2 isn't that much code either, the complexity comes from trying to support lots of versions -- and from X.509 which has a lot of stuff to process.

I think Chrome for Android did include TLS 1.2 at least, when it was shipping for Gingerbread.